UC-NftLF 



INTROJ 



MECHANICAL 




J C TRACY E 

Sf t * * I V \ >' ' Vt- 



ft n r_ 






REESE LIBRARY 

in 

UNIVERSITY OF CALIFORNIA. 
ctyceived 







INTRODUCTORY COURSE 

IN 



MECHANICAL DRAWING 



BY J. 0. TRACY, C.F, 

INSTRUCTOR IN THE SHEFFIELD SCIENTIFIC SCHOOL OF YALE UNIVERSITY 



WITH CHAPTER ON* PERSPECTIVE 

BY E. H. LOCKWOOD, M.E. 

INSTRUCTOR IN THE SHEFFIELD SCIENTIFIC SCHOOL 





NEW YORK AND LONDON 

HARPER & BROTHERS PUBLISHERS 

1898 



A 



Copyright, 1898, by HARPER & HROTHERS. 



All right* reserved. 



PREFACE 




THIS book is intended for beginners. Its aim "is to prepare the 
student for a more extended course in any one of the special lines 
of drafting. The endeavor has been to make the book comprehen- 
sive enough for use in schools and colleges, and, at the same time, 
to have it meet the needs of the student who must study the sub- 
ject with little if any help from a teacher. In the preparation of the 
work the author has assumed : 

1. That those who will use the book will have a working knowl- 
edge of, at least, the elements of geometry. 

Hence geometrical definitions and constructions are omitted. 

a. That machine drawing, bridge drawing, and other more ad- 
vanced applications of mechanical drawing are better omitted from 
a course designed to be introductory to any kind of instrumental 
drawing. 

3. That the success of any course depends largely upon the nature 
of its problems. 

Hence each problem lias been chosen for some definite principle it illustrates, and 
the whole so arranged as to form a progressive series. (See introduction to problems, 
page 1.) 

4. That information worth giving to the beginner is worth giving 
in book form. 

Hence the numerous and explicit directions and suggestions of the first three chap- 
ters, so grouped and arranged as to be easy of reference. 

5. That in teaching mechanical drawing there is a legitimate use 
for models. 

Hence the insertion of photographs throughout the book. The advantage of these 
photographs over ordinary models is obvious. 



IP. That orthographic projection, because of its importance, should 
have the fullest and most systematic treatment. 

7. That in the treatment of orthographic projection a few of 
the fundamental principles of descriptive geometry must be mado 
clear. 

The use of photographs of models enables this to be done without plunging 
the student beyond his depth in abstract theory (Chnps. V. and VI. See Art. 65, 
page 47). 

8. That a chapter of concise practical directions Tor perspective 
drawing will be welcomed by students and draftsmen who do not 
care to study a more extended treatise on the subject. 

The author's friend and colleague, Mr. E. H. Lockwood, has had 
no small part in the preparation of this book. Mr. Lockwood and the 
author originally planned to write it together. Prevented from sharing 
in the actual work, the former has had at all times an author's inter- 
est in the book's success. He has placed at the author's disposal his 
pamphlet on Mechanical Drawing, and Chapter V. is a revision of a 
similar chapter in this pamphlet. In addition, Mr. Lockwood has 
kindly contributed Chapter VII.. on perspective. 

The author is also indebted to the following graduates and students 
of the Sheffield Scientific School : Messrs. Patterson, Hopton, Rogers, 
Hastings, Howarth, and Weaver, for contributing the drawings at the 
end of the book ; and to Mr. L. D. Tracy, for checking the wording and 
dimensions in the manuscript of the problems. 

J. C- TRACY. 

NEW HAVEN, November, 1S97. 



TABLE OF CONTEXTS 



PROBLEMS 




Introductory 1 

Special Directions for Making Plates 2 

PLATE I. Straight Lines and Geometrical Constructions 2 

Opti'iinul I. Freehand Lettering and Geometrical Design 3 

PLATE II. Isometric Projection 'A 

Optional II. Isometric Drawing of Card File, Tool Chest, or Other Similar 

Object 4 

PLATE III. Cabinet Projection 5 

Optional III. Line-shading 5 

PLATE 1 V. Isometric and Cabinet Projection Circles 6 

Optional IV. Same as Optional II., except the Drawing is in Cabinet Pro- 
jection 6 

PLATE V. Orthographic Projection of Point and of Lines Perpendicular to H or V 6 
Optimaii I'. Isometric and Cabinet Drawings of Objects with Cylindrical 

Surfaces 7 

PLATE VI. Lines Parallel to One Plane of Projection at an Angle with the Other 7 

Optional IT. To Find Axes of Ellipse in Cabinet Projection 7 

PLATE VII. True Length of a Line, and a Line Making Given Angles with H 

and V 7 

Optional VII. Problem when the Sum of the' Angles a Line Makes with II 

and V equals 90' 8 

PLATE VIII. Orthographic Projection Solids in Kasy Positions 8 

Optional VI II. To Find True Shape and Size of a Face of a Solid 9 

PLATE IX. Orthographic Projection Same Solid in Different Positions Practice 

in Showing Invisible Lines 9 

Optional IX. Working Drawing of a Box ' 9 

PLATE X. Orthographic Projection End Views 9 

Optional X. Working Drawing of a Card File 10 

PLATE XI. Orthographic Projection Side Views 10 

Optional XI Working Drawing of liox wiili Sloping Sides 10 

PLATE XII. Orthographic Projection of Solids Previously Drawn in the Plates 

on Isometric and Cabinet 10 

Optional XII Working Drawing of a Carpenter's Bench 11 



PLATE XIII. Orthographic Projection Solids Inclined to H and V 11 

Opt im,, il XIII. Floor Plans for a House H 

PLATE XIV. Solids Inclined to H and V 11 

Optional XIV. Views of a Bridge Pier on a Skew 12 

PLATE XV. Curves : Ellipse, Hyperbola, Parabola 12 

Optional XV. Views of the Cube of 4 (H), Plate II., no Face Parallel to II or V 13 

PLATE XVI. Plane Sections 13 

Optional XVI. Working Drawing of Printing. frame or Book-case with Sec- 
tional View 13 

PLATE XVII. Plane Sections 13 

Optional XVII. Square Prism Section Cut by a Plane at an Angle with Hand V 14 

PLATE XVIII. Conic Sections 14 

Optional XVIII. Line-shading 14 

PLATE XIX. Intersection of Two Cylinders 14 

Optional XIX. To Make Two Intersecting Cylinders of Card-board 15 

PLATE XX. Intersections: Spheres, Cylinders, Hexagonal Prisms, and Develop- 
ments 1 o 

Optional XX. Card-board Intersection of Two Cylinders Oblique to Each Other 15 

PLATE XXI. Intersections: Oblique Cylinders Cone and Cylinder 15 

Optional XXI. Working Drawing of a Box with Holes for a Pipe Passing 

Diagonally through It 16 

PLATE XXII. Shadows on H 16 

Optional XXII. Isometric Shadows 16 

PLATE XXIII. Shadows 16 

Optional XXIII. Shadow of Cylinders and Exercise in Graded Tints 17 

PLATE XXIV. Perspective '... 17 

Opt/iiniif A"A7 T. Shadow of Cone on Cylinder Graded Tints 18 

PLATE XXV. Perspective Drawings of Solids Previously Drawn in Isometric 

and Cabinet (Plates II. and III.) 18 

Optional XXV. Perspective Drawings of Solids with no Face Parallel to 

Picture Plane 18 

PLATE XXVI. Perspective Drawings of Solids with Circular Outlines 18 

Optional XXVI. Perspective Drawing of a House 18 



VI 



TABLE OF CONTENTS 



CHAPTER I 

THE SELECTION OF THE OUTFIT 

The Selection of the Outfit 19 

List of Instruments and Materials Required 19 

Tlie Compasses 20 

The Ruling-pen 20 

Care of Instruments 20 

T-square - 21 

Triangles 21 

Scale 21 

Inks 21 

Drawing-boards 21 

Drawing-paper 21 

Miscellaneous 21 

Summary: Estimated Cost of Outfit 22 



CHAPTER II 

THE USE OF THE DRAWING INSTRUMENTS 

The Pencil 23 

The T-square 23 

The Triangles Vertical Line Lines Making a Given Angle with the Horizontal 

Lines Parallel to a Given Line 24 

Lines Perpendicular to a Given Line 25 

The Ruling-pen 25 

The Compasses 27 

The Dividers 28 

The Scale 28 

Architects' Scale 29 

Curve-ruler 29 



CHAPTER III 

WORKING KNOWLEDGE 

To Fasten the Paper to the Board 30 

Precautions to Insure Neatness 30 

Arrangement ' 30 

Rapid Drafting 31 

Pencilling 31 

Inking 31 

Erasing 32 



Laying off Measurements 32 

Use of Triangles 33 

Line Notation 33 

Lettering the Drawing 33 

The Use of Colored Inks 34 

To Mix India ink 34 

Shade Lines 34 

Line-shading 34 

Parallel-line Shadows 35- 

Section Lines 35 

Tinting 35 

Graduated Tints 36 

Blue-print Process 36 

Tracings 37 

Blue Process Paper 37 

Miscellaneous Geometrical Constructions To Plot an Angle; To Draw a False 

Ellipse ; True Ellipse ; Parabola 38 

Hyperbola 39 



CHAPTER IV 

ISOMETRIC PROJECTION AND CABINET PROJECTION 

Difference between Isometric, Cabinet, and Perspective 40 

Isometric Projection Fundamental Principles Axes 40 

Non-rectangular Objects in Isometric Projection 41 

Isometric Scale 41 

Circles in Isometric 41 

Irregular Curves in Isometric 42 

Shadows in Isometric 42 

Cabinet Projection Fundamental Principles Axes 42 

Rules for Cabinet Projection 43 

Circles in Cabinet Projection 43 

Oblique Projection 43 

Isometric Projection and Cabinet Projection Compared 44 

Advantages and Disadvantages of Isometric and Cabinet Projection 44 



CHAPTER V 

ORTHOGRAPHIC PROJECTION 

Projection Definitions 45 

Orthographic Projection 45 



TABLE OF CUXTKNTS 



vii 



Angles of Projection 

Views Different Terms ; How the Views are Determined 

Ground Line 

The Drawing To Represent, the Planes of Projection; The Relative Positions of 

Different Views 

l".-e of Photographs of Models 

A Point in Space; 

Straight Lines Perpendicular to II or V 

Straight Lines Parallel to One Plane of Projection but at an Angle with the Other. 

Lines Parallel to Both II and V, and Lines Parallel to Neither II nor V 

Profile Plane 

To Find the True Length of a Line and the Angle it Makes with II or V 

Given: The Angles a Line Makes with H and V to Fiud the Views of the Line. . . 

Plane Figures 

Boundary Lines and Surfaces of Solids 

Solids in Orthographic Projection 

Square Prism in Orthographic Projection 

Assuming the Position of an Object 

Additional Views End View Square Prism 

End View Cylinder 

End View Hexagonal Prism 

Side View Hexagonal Pyramid 

Invisible Edges 

Square Prism ; Face at an Angle with V , 

Solids Inclined to II and V 

Square Prism Inclined to II and then to V 

Hexagonal Prism Inclined to V and then to II 

Planes and Traces of Planes 



PACE 

45 
46 
40 

40 
47 
48 
50 
58 
54 
55 
55 
55 
56 
56 
57 
57 
57 
58 
59 
60 
60 
61 
61 
61 
63 
65 
67 



CHAPTER VI 

SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 

SURFACES OK KKVOLCTIOS, PI.ANK SKCTIONP, IXTKRSKCTIOXS, AND SHADOWS 

Circle Inclined to II and V 68 

Given : One View of a Point on a Surface of Revolution to Find the Other View . . 69 

Plane Sections 70 

Cylinder Axis Parallel to H and V ; Plane Parallel to V 70 

Cylinder Axis Perpendicular to H ; Plane Parallel to V 70 

Sphere Plane Parallel to V 71 

Sphere Plane Perpendicular to H, at Angle with V 71 

Square Prism Base Parallel to II; Plane Perpendicular to V, at Angle 

withH.. , 72 



Cylinder Axis Perpendicular to \" ; Plane Perpendicular to II, at an Angle 
with V 

Cylinder Axis Perpendicular to 11, Plane Parallel to the Ground Line 

Couic Sections 

Square Prism Face at an Angle wiih V; Axis Perpendicular to H; Plane at 
an Angle with II, Perpendicular to V 

Hexagonal Pyramid Axis Vertical ; Plane Parallel to V 

Intersection of Surfaces 

General Method 

Two Cylinders 

Cylinder and Sphere 

Cylinder and Cone 

Cylinder and Hexagonal Prism 

Hexagonal Prism and Sphere 

Development of Surfaces 

Cylinder 

Cone 

Shadows 

To Find where Any Ray of Light Pierces II or V 

Shadow of a Square Prism on II 

Rules for Shadows ; 

Shadow of a Square Prism on Both II and V 

Shadow of a Hexagonal Prism on II 

Shadow of a Cylinder on H 

Shadow of Two Blocks on II 

Shadow of a Circle Parallel to V 

Shadow of a Circle Perpendicular to H and V 

Shadow of One Object upon Another 

Shadow of a Part of an Object on Another Part 

Shadow of a Cone upon a Cylinder 

Shade Lines, Rules for 

Darkest and Lightest Portions of Curved Surfaces 



72 
72 

72 



75 
76 
76 
76 
78 
7iJ 
80 
80 
80 
80 
80 
81 
81 
82 
82 
82 
83 
83 



83 
84 
84 
84 
85 
86 



CHAPTER VII 

PERSPECTIVE 

Introductory 87 

Perspective Drawing Defined 87 

Picture Plane 88 

Point of Sight 88 

Elementary Constructions 88 

Lines in Special Positions .' 88 



TAHLK OF CO.NTKNTS 



Horizon 89 

Points of Distance 89 

Vanishing Points 89 

Construction of the Drawing 89 

Reduced Points of Distance 90 

Circles in Perspective 91 

Spacing Equal Distances 91 

Choosing the Point of Sight and Points of Distance 91 



CHAPTER VIII 



WORKING DRAWINGS 



Working Drawing Defined 93 

Arrangement of Views 93 

Method of Making the Drawing 94 



Method of Giving Dimensions 94 

Notes of Explanations and Directions 96 

Titles 97 

Suggestions 97 



PLATES 

I. Working Drawing of a Card File 101 

II. Working Drawing of a Desk 103 

III. Examples of Line Shading 105 

IV. Cabinet Projection of a Drawing Desk 107 

V. Isometric Projection of a Tool Chest 109 " 

VI. A Plate Showing Orthographic Projection Illustrated by Isometric Pro- 
jection Ill 

VII. Perspective Drawing (if a Shore Cottage 113 

VIII. Screw Threads and Standard Cross Suctions 115 




AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



PROBLEMS 



INTRODUCTORY 



THE problems here given constitute two distinct but parallel courses of 
twenty -six plates each. Any problem of course a, can be substituted for the 
corresponding problem of the same plate, course b, or vice versa, without affect- 
ing the general plan. The courses a and b are, therefore, equivalent, and either 
one can be pursued, or a combination of both, thus enabling different plates to 
be arranged from year to year. The principles which these problems illustrate 
are explained in the succeeding chapters. The general directions for drawing 
the plates are given on page 2. 

The problems for the most part are limited to geometrical solids, because 
these are easily described in print. The solids, however, are so combined as to 
furnish new and useful variations in many cases. The advantage to the student 
of drawing an object solely from a printed description is obvious. 

In general, two exercises of one and one-half hours each will be required- for 
a plate. The first three plates and two or three others may require additional 
exercises. From ninety to a hundred hours should be a sufficient time in which 
to complete either course as given. An instructor can easily adapt the course to 
longer or shorter exercises by changing the number of problems on a plate. 
Since each plate is divided into as many equal parts as there are problems, it is 
easy to estimate how much space should be allowed for each problem. Though 
the plates are intended to be 22" x 15", with a 21"xl4" border line, this size 
can be changed if the number of problems on each plate is also changed. 

Only three plates are given in isometric and cabinet, as practice in these 
projections will be gained in illustrating orthographic projection. If time will 
1 



allow it is a good plan to draw Plate II. in cabinet and Plate III. in isometric, 
thus introducing an additional plate in each of these projections. 

In connection with the required course there is an optional course, consist- 
ing of drawings to be made outside of the regular exercises. This course aims 
to give practical applications of the principles taught in the regular course. It 
is designed for those students who intend to pursue one of the courses in engi- 
neering, as well as for all others who desire to gain a more practical knowledge 
of drawing than they otherwise would. Great freedom should be allowed in 
this course, and the student should be encouraged in original work. In this 
way the student can begin to make " working drawings." The instructor can 
by personal supervision make this part of the course of great value. By intro- 
ducing optionals the required course can be lengthened ; by omitting certain 
plates it can be abridged. Few beginners will be able to draw all the option- 
als ; the instructor can recommend to each student those which will be of the 
most value to him. 

The notes at the end of each plate are designed to aid the student. In 
many cases they warn him against common mistakes. The instructor should 
insist on the student reading these notes and studying the articles referred 
to in connection with a plate before beginning to draw that plate. The direc- 
tions, which are numerous at first, decrease in number as the course progresses, 
and the student is better able to work without assistance. 

Isometric and cabinet projections have been used in many plates to illus- 
trate problems in orthographic projection. The finished figure or picture which 
results in any particular case is, perhaps, of little value. The work necessary in 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



drawing it, however, is of great value to the student in understanding orthographic 
projection. The instructor, however, should make it clear at the beginning that 
this is of no practical benefit after a knowledge of orthographic projection has 
been acquired. This method of teaching orthographic projection is unusual, 
but it has been tried with such success as to warrant its introduction in this 
course. 

Special Directions for Making Plates. For each plate of this course 
there will be a border line 14"x21". The space within this border is to be 
subdivided into as many smaller equal rectangles as there are problems. Each 
figure is to be located symmetrically with respect to the sides of its own rec- 
tangle. See Art. 25 (c). When thought desirable the figure has been more 
definitely located by two co-ordinate distances (x and y) of sotne starting-point 
from the left-hand and lower sides of the rectangle ; x represents the distance 
of this point from the left-hand side, and y from the lower side of the rectangle. 
Unless otherwise noted the starting-point is the lowest point of the figure ; if 
there are two or more such points, the left-hand lowest point is chosen. 

An article or note referred to at the end of a problem has special bearing 
on that problem. Never begin a plate or problem without reading the articles 
and notes thus indicated. 

Problems are to be arranged in order lengthwise across the paper, each row 
beginning at the left-hand edge. 

The number of the plate, as, for example, Plate I., should be printed below 
the centre of the upper edge of the paper, just above the border line, in letters 
about T 2 U " or -fa" high. Ink in the border line about -fa" wide, and the lines 
between the different problems about as light as the pen will draw. 



PLATE I 

1 (a). Draw twelve horizontal lines, one under the other, 3^" long and J" 
apart. At right angles to these, draw eight lines " apart, thus forming a rec- 
tangle 2|-" wide by 3^" long, composed of seventy -seven smaller rectangles 

i" b y f. 

1 (b). Draw a rectangle the horizontal sides of which are 3" long, the ver- 
tical sides ]". Draw a second rectangle the horizontal sides of which are 1" 
long, the vertical sides 2J". The centres of the two rectangles coincide. Sub- 
divide the first rectangle by horizontal lines 3" long and J" apart. Subdivide 
the second rectangle by vertical lines 2J" long and " apart. The finished fig- 



ure will then be composed of thirty -six " squares, twelve |/'xl" rectangles, 
and twelve |"x V rectangles. 

2 (a). Draw the figure of 1 (a) when the parallel lines in one direction are 
30 lines; the parallel lines in the other direction will then be 60 lines. 
x = 'ty", y=". (Notea.) 

2 (b). Draw the figure of 1 (b) when the parallel lines in one direction are 
30 lines ; the parallel lines in the other direction will then be 60 lines. 
(Note b.) 

3 (a). Draw the figure of 1 (a) when the parallel lines in one direction are 
45 lines; the parallel lines in the other direction will also be 45 lines. 
*=8f',y=i". 

3 (6). Draw the figure of 1 (b) when the parallel lines in one direction are 
45 lines; the parallel lines in the other direction will also be 45 lines. 

4 (a). Draw the figure of 1 (a) when the parallel lines in one direction are 
15 lines; the parallel lines in the other direction will then be 75 lines. 



4 (&). Draw the figure of 1 (b) when the parallel lines in one direction are 
15 lines ; the parallel lines in the other direction will then be 75 lines. 
(Notec.) 

GEOMETRICAL CONSTRUCTIONS 

5 (). Given a horizontal line 4" long. At the centre of this line erect a 
perpendicular line extending 1|^" above and 1-ff" below the given line. Use 
the compasses only in finding the perpendicular. 

5 (b). Same as 5 (a), except that the given line is a 30 line. 

6 (a). A 30 line 3 T y long and a 75 line 3^-J." long meet in a point, form- 
ing an acute angle. By means of the compasses bisect this angle by a third 
line 4|" long. xl^", y=^$" (to vertex of angle). (Note d.) 

6 (b). Same as 6 (a), except that the given lines are 15 and 60 lines re- 
spectively. x=l", y~y (to vertex of angle). (Noted.) 

7 (a). Given a 30 line 3-^" long. Divide it by a geometrical construction 
into nine equal parts. x=\^", y^". (Note.) 

7 (b). Same as 7 (a), except that the given line makes any unknown angle 
with the horizontal. (Note .) 

8 (a). Given a circle 2" in diameter. From any point 3^" from the centre 
of the circle draw two geometrically constructed tangents to that circle. 
x=l^", y 2 T 5 T " (to centre of circle). 



PROBLEMS 



' 



8 (l>). Same as 8 (a), assuming the point anywhere outside the circle. 

9 (a). Draw a 4" circle and by means of the protractor inscribe a pentagon. 

9 (A). Draw a 4" circle and by means of the protractor inscribe a nonagon. 

10 (n). Using only the scale, T-square, and triangles, draw a hxagon two 
sides of which are vertical. The length of a side is 2". 

10 (4). Using only the scale, T-square, and triangles, draw a hexagon two 
sides of which are horizontal. The length of a side is 2". 

11 (a). Using only the scale, T-square, and triangles, draw an octagon two 
sides of which are horizontal. The length of a side is 1". (Note/.) 

1 1 (If). Using only the scale, T-square, and triangles, draw an octagon no 
side of which is horizontal. The length of a side is 1". (Note/.) 

12 (). Draw a 4" circle. Using only the T-square and triangles, divide 
this circle into twenty-four equal sectors. (Note#.) 

12 (i). Draw a 4" square ; from each of its corners draw an arc of a circle 
terminating in the middle points of two sides of the square. Divide each 
quadrant of a circle thus formed into six equal parts, using only the T-square 
and triangles. 

NOTES PLATE I 

This plate is given to practise the student in the use of the instruments. It is to 
be drawn in pencil at the first exercise and inked in (it the second. 

EXERCISE 1 

Before beginning this exercise read Arts. 14-16, 18 (a), (b), (c), 19, 20 (a), 23-27, 
29-32, and the special directions for making plates, page 2. 

Draw a border line 14" x21" and divide the enclosed space into twelve equal spaces. 
Place first four figures in the upper row. 

() In 2 (a), 3 (), and 4 (a) the larger portion of the figure is to the left of the point 
located by .r and y. 

(V) In 2 (b), 3 (b), and 4 (b) the centre of each figure is in the centre of its rectangle. 

(e) See Art. 16 (e). Pigs. 4 and 5. and Arts. 16 (d), (<), (/) , Figs. 6, 7, and 8. 

(rf) In 6 (ft) and 6 (6) both lines forming the angle extend to the right of the point 
located by x and y. 

(f) In 7 (a) and 7 (b) use triangles for drawing the parallel lines. See Art. 16 (d). 
(/) In 11 (a) and 11 (b) the distance between any two parallel sides of the octagon 

is about 3f ". 

(g) See Art. 16 (c). 

EXEKCISE 2 

Before inking the plate read carefully Arts. 17, 18 (d), (e), (f), (g). 28, 29 (4), (c), 33. 
In geometrical problems ink in given and required lines full. Construction lines 



are small, fine dashes. See Art. 32 (b). The student 4S to use his judgment in lettering 
geometrical figures to make them clearer. For example, in Prob. 6 (a) it might be well 
to print on the lines "30" LINE," "75 LINE," and " BISECTOK" respectively. 
See Special Directions, page 2, for title anil border lines. 

OPTIONAL 

1 (a). FREE-HAND LETTERING. Print the lower-case letter . (See Fig. 9, 
Reinhardt's book on lettering. See Art. 33.) Indicate by numbers and arrows 
tl|e sequence and directions of the strokes, leaving small breaks between the 
strokes. This shows the method of forming the letter. Under this a print a 
horizontal line of several a's, omitting numbers, arrows, and breaks. Treat 
each letter of the lower-case alphabet and each capital letter in a similar man- 
ner. Make the letters about the same size as those in Reinhardt's book. Use 
not more than two pencil guide-lines, one for the top and one for the bottom 
of the letters. The arrangement of the whole plate is left to the taste of the 
student. 

When the student can do this optional well the instructor can arrange sev- 
eral others, including one which groups the letters into words, and one on 
letters of the Block, Egyptian, and Roman systems, made free-hand and with 
the instruments. If time allows it is well to give a course in lettering as part 
of the regular required course. 

1 (b). [To he drawn instead of 1 (a) when lettering is part of the required 
course.] Draw an original geometrical design of straight lines, circles, and 
arcs of circles. Aim at symmetry and accuracy as well as a graceful, pleasing 
effect. 



PLATE H 

ISOMETRIC PROJECTION 

Make an isometric drawing of: 

1 (). A rectangular block I"xl"x3" standing on 



" end. 



1 (b). The same block as in 1 (a) when it is lying on a I|"x3" face. 
=*!f',y=l|". 

2 (rt). A block 2-J." square and J" high ; in the centre of the upper face of 
this block stands a second block 1-J" square and J" high ; in the centre of the 
upper face of the second block stands a third block " square and f" high. 
The corresponding edges of the three blocks are parallel, a- 3", ?/ 1-|". 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



2 (b). A block 1" high; the base on which it stands is If x 3" ; the top 
face is I"x3"; the two sides have the same slope. x=2^", y=l||". 

3 (a). A block f" high; the lower base is 1" square; the upper base is 1" 
square; the sides all have the same slope. Standing on this block is a prism 1" 
square and 2" high, upon the top of which rests a third block exactly like the first 
except it is inverted, its 1" square base coinciding with the upper base of the 
prism. The centres of all bases are in a straight line. z=3|", y = l". (Note a.) 

3 (b). Same as 3 (a) when the axis passing through the centres of the three 
blocks is horizontal instead of vertical, x 2f", y=l|". (Note a.) 

4 (a). A hollow 2" cube ; the thickness of sides is \". In the centre of 
each face is an open hole 1" square ; the edges of the holes are parallel to the 
corresponding edges of the cube. x=3%", y=l". 

4 (6). A hollow hexagonal prism 3" long ; a side of the outside hexagon is 
J" long. The perpendicular distance between the outside and inside surfaces 
is ^5-". Half-way between the two ends there is a continuous raised rectangu- 
lar strip 1" wide by ^" thick extending entirely around the outside of the 
prism. The 1" is measured parallel to a 3" edge of the prism. Assume two 
faces of the prism to be horizontal, the two ends of the prism being vertical. 
ar=4", y=lf" (to corner of rectangle in which largest hexagon of right end is 
inscribed. Figure extends to the left). (Note b.) 

5 (a). A solid which has for its front end a rectangle 2" wide by 1|" high; 
its rear end is 2" wide by 2" high ; the perpendicular distance between the 
two ends is 3J" ; the four sides all have the same slope. Through the centre 
of each of these four sides there is a groove J" deep (measured parallel to ends 
of block), running lengthwise. These grooves are each \" wide at the smaller 
end of the block and f " wide at the larger end. Assume the two ends of the 
block to be vertical. z=2f", y=\^". 

5 (b). A 2" cube; in the centre of each face there is a raised block 1" 
square by J" thick. The edges of the blocks are parallel to the corresponding 
edges of the cubes. z=3J", y = l". 

6 (a). A hexagonal prism 3" high; side of hexagon 1"; prism stands on a 
hexagonal end. Half-way up the prism there is a rectangular groove 1" wide by J" 
deep extending entirely around the prism at right angles to its edges. x=S^", 
y=y (to the corner of rectangle in which lower base is inscribed). (Note 4.) 

6 (b). A hexagonal pyramid 3" high ; side of hexagonal base is 1 J" long. 
Half-way up the sides of the pyramid is a groove extending entirely around 
the pyramid. This groove is formed by removing the portion of the pyramid 



between two cuts, eacli " deep. The planes of both cuts are parallel to the 
plane of the base of the pyramid. The perpendicular distance between the 
planes of the two cuts is 1". a;=3 T 5 ", y=l T 3 " (to corner of rectangle in 
which base is inscribed). (Notec.) 

NOTES PLATE II 

Before beginning the plate, study Arts. 46, 47, 48. 

The distances given for x and y hold good in unsymmetrical figures only when the 
larger portion of the figure extends to the right of the point located. See Art. 47 c. 
An exception is in 4 (b). 

The edges which cast shadows should be represented by heavier lines than are the other 
edges (Art. 53). First draw all light lines on the plate with one setting of the pen, and 
then draw shade lines. Thus, if a mistake is made in the first set of lines, it is more easily 
corrected than if heavy lines were drawn first. Do not make shade lines too heavy. 

(a) In 3 (a) the }" is the perpendicular, not the slant height. The front edge of the 
lower block will therefore be longer than ". See Fi.c. 22, page 41. 

(b) In 4 (b) and 6 (a) draw on a waste piece of paper a true hexagon, and proceed 
according to Art. 48. 

(c) In 6 (b) it is evident that the portion of the pyramid removed is not J" thick 
the \' being measured parallel to the plane of the base. The groove, likewise, is 
more than 1" wide if measured parallel to the plane of a side face. 

OPTIONAL II 

Make an isometric drawing of one of the following objects: 

1 (a). A shallow box (about 8" square and 2" deep) divided into four 
equal compartments by two cross-pieces at right angles to each other. The 
ends of the cross-pieces set into vertical grooves in the sides of the box. Each 
cross-piece is notched half its depth for the other cross-piece. 

1 (b). Same as 1 (a) except that the bottom of the box is smaller than the 
top and the sides all have the same slope. 

1 (c). A box with drawer or drawers for a card catalogue. 

1 (d). A printing-frame for photographs. 

1 (e). A small book-case or set of book-shelves. 

1 (/). A small cabinet for minerals. 

1 (</). A flower-stand. 

1 (h). A tool-chest. 

XOTE. Original designs are preferable to drawings made from measurement. Dimensions 
may or may not be given on the drawing. Any simple rectangular object approved by the in- 
structor may be chosen in place of one given if the student so desires. 



PROBLEMS 



PLATE III 

CABINET PROJECTION- 

Make a drawing in cabinet projection of : 

1 (a). A rectangular block 2" high standing on a base 3" square. In the 
centre of the upper face there is a rectangular hole 2" square by $" deep ; the 
edges of the hole are parallel to the corresponding edges of the block, x 

iA",y=2". 

1 (b). Same block as in 1 (a) when it is standing on a 2" by 3" face. Let 
the face with the square hole be the side face shown, x 2", y=l". 

2 (). Three cylinders, A, B, and C, each 1" long; cylinder A is 1" in 
diameter, B 2" in diameter, and C 3" in diameter. These cylinders are all 
horizontal, with their axes in the same straight line at right angles to the plane 
of the paper. The rear end of A is in contact with the front end of B, and the 
rear end of B is in contact with the front end of C. Thus the distance from 
the front end of A, which is in the plane of the paper, to the rear end of C is 
4". ar=2-j^", j/ = 2 T ^" (to centre of circle in plane of paper). 

2 (b). Same problem as 2 (a), substituting hexagonal prisms for the 
cylinders. The lengths of the sides of the hexagons are: For prism A ^", 
prism B I", prism C 1J". jr=2-^ ff ", y^=2fy" (to centre of hexagon in plane 
of paper). 

3 (a). A rectangular block 4" square by 1-f" high. In the upper face of the 
block are four rectangular holes, each 1|-" square by J-" deep; the edges of the 
holes are parallel to the corresponding edges of the block, and the distance be- 
tween any outside edge of a hole and the nearest edge of the block is ". x\ ", 

y=3tV'- 

3 (b). Same block as in 3 (a) when it is standing on a 1|" x 4" face. Let 
the face with the square holes in it be the side face shown. #=2", y= J". 

4 (a). A rectangular block 4" square by 1^" high. In the upper face there 
are two rectangular grooves 1" wide by J-" deep running diagonally from corner 
to corner at right angles to each other. The centre line of each groove coin- 
cides with the corresponding diagonal of the upper face of the block. a'=J", 

y=2". 

4 (b). A rectangular block 4" square by 1J" high with raised diagonal 
strips 1" wide by J" high (total height 1"). The block in this problem is the 
reverse of that in 4 (a), the raised portion of 4 (6) fitting the grooves of 4 (a). 



5 (a). A rectangular block 4" square by " high. In the centre of the 
upper face of this block stands the frustum of a hexagonal pyramid. A side 
of the hexagon of the lower base is 1" ; of the upper base J". Two sides of 
the lower hexagon are perpendicular to the front edge of the rectangular block. 
The frustum is 2" high. z=", y=l|". 

5 (b). The prisms of 2 (6) when the common axis of the three prisms is 
vertical instead of horizontal. Let the largest prism be at the bottom, and let 
two faces of each prism be parallel to the plane of the paper. x=lfa", y=l" 
(to corner of rectangle in which lowest base is drawn). 

6 (a). A 2J" cube. A continuous raised strip " wide by -J-" high passes 
through the centres of the front, top, back, and bottom faces parallel to two 
sides of each face. There are two similar strips around the cube one through 
the centres of the top, side, and bottom faces ; the other through the centres of 
the front, side, and back faces. a-=l|",y 1|" (to corner of cube). 

6 (b). A 3" cube. Through the centres of the front, top, back, and bottom 
faces there is a continuous groove J" wide by ^" deep. The groove is parallel 
to two sides of each face of the cube. There are two similar grooves around 
the cube one through the centres of the top, side, and bottom faces ; the other 
through the centres of the front, side, and back faces. x = \%", y 1 J". 

NOTES PLATE III 

Before beginning the plate, study Arts. 54 and 55. 

x and y are given for figures which extend to the right of the point located (Art. 
54 b). 

Begin Figs. 2 (a) and 2 (b) by drawing a 45 line from the point located. The 
centres of all circles or hexagons will be on this line. (Why ?) 

Begin all figures in which there are grooves or raised strips by drawing the object 
first, subsequently cutting out the grooves or adding the strips. Omit lines where 
raised strips intersect each other except those lines which are necessary to show the 
corners. 

Shade' the edges which cast shadows, as in isometric. In 2 () shade the lower 
right-hand quadrant of front circles (see Art. 36 b). This figure may also be improved 
by shading with parallel lines to make the surfaces appear cylindrical (Art. 37). 

OPTIONAL III 

1. Draw a rectangle about 2" wide and 5" high, and shade it with line- 
shading to represent a vertical cylinder. See Art. 37. 

2. Shade a rectangle 2" high by 5" long to represent a horizontal cylinder. 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



PLATE IV* 
ISOMETRIC AND CABINET PROJECTION 

1 (a). Make an isometric drawing of the frustum of a cone; the lower base 
is 3" in diameter, the upper base 2" in diameter; the height of the frustum 
(perpendicular distance between the two bases) is 3". Use the isometric scale, 
a; 5J", y = l^g" (to corner of square in which base is inscribed). 

1 (b). Make an isometric drawing of two cylinders, one on top of the other. 
The lower cylinder stands on a base 3" in diameter and is 2" high ; in the cen- 
tre of its upper base stands a second cylinder 2" in diameter and l"high. Use the 
isometric scale. z = 5", y=lfa" (to corner of square in which base is inscribed). 

2 (a). Make a cabinet drawing of the frustum of 1 (a), x 3^", y \^" 
(to corner of square in which the base is inscribed). 

2 (b). Make a cabinet drawing of the cylinders of 1 (b). r=3", y = \-fo" 
(to corner of square in which the base is inscribed). 

3 (a). Make an isometric drawing to isometric scale of a 3" cube ; in the 
centre of each face there is a circular hole 2" in diameter by J-" deep. x=5^", 

y=i T V". 

3 (6). Make an isometric drawing to isometric scale of a 3" cube ; in the 
centre of each face there is a raised circular block 2" in diameter by J" thick. 

*=5J", y=W. 

4 (a). Make a cabinet drawing of the cube of 3 (a). x=3^", y=l^". 
4 (b). Make a cabinet drawing of the cube of 3 (b). x 3-^", y = l^". 

NOTES PLATE IV 

Study Arts. 49, 50, 51, 56, 57, and 58. 

Every figure in this plate contains circles which project into ellipses. Draw the 
circumscribed square in each case, except in 3 (a) and 4 (), where the part of the 
inner ellipse which shows can be made most easily by shifting the outer ellipse parallel 
to itself. 

A good comparison of the two projections is afforded by this plate. Either may be 
advantageously used to represent objects to persons not skilled in reading ordinary 
working drawings. So-called " show drawings" (as compared to working drawings) are 
therefore often made in one of these two projections. 

OPTIONAL IV 

Make a cabinet drawing of one of the objects given in Optional II. 
Any similar object approved by the instructor may be chosen instead. 

* In abridged courses tliis plate may be given as an optional. 



PLATE V 
ORTHOGRAPHIC PROJECTION ILLUSTRATED BY ISOMETRIC PROJECTION 

Represent by means of isometric projection the following point and 
lines, together with the top view and front view of each on H and V re- 
spectively : 

1 (a). A point 1 in space 1" behind V and 2" below H. (Notes a and b.) 

1 (b). A point 1 in space 2" behind V and 1" below H. (Notes a and b.) 

2 (a). A straight line 2-3 2^" long, perpendicular to H and 1" behind V. 
One end of the line is in H. (Note d.) 

2 (b). A straight line 2-3 2" long, perpendicular to II and IJ" behind V. 
The upper end of the line is " below II. 

3 (a). A straight line 4-5 2" long, perpendicular to V and 1^" below H. 
The nearer end of the line is " behind V. 

3 (b). A straight line 4-5 2" long, perpendicular to V and 1" below II. 
One end of the line is in V. (Noterf.) 

Draw the top view and front view in true orthographic projection of: 

4 (). The point 1 of 1 (). (Note c.) 

4 (b). The point 1 of 1 (b). (Note c.) 

5 (a). The line 2-3 of 2 (a). 

5 (b). The line "2^3 of 2 (/>). 

6 (). The line 4^5 of 3 (a). 
6 (b). The line 4^5 of 3 (b). 

NOTES PLATE V 

Study Arts. 59-69 (d) inclusive. 

Draw a border line 21" x!4" and divide the enclosed space into six 7" squares, one 
for each problem. Draw the first three problems in the upper row. Place (4) under 
(1), (5) under (2), and (6) under (3). 

Commence each of the first three problems by drawing the three isometric axes 
from the centre of the 7" square, the vertical axis extending downward. Make the <"< * 
each 3" long, and construct upon them two planes corresponding to the top and the left- 
hand front faces of an isometric cube. Let these planes represent a portion of the two 
planes of orthographic projection (which are in reality of infinite extent), forming togeth- 
er the third angle of projection. The given point or line is located in this angle accord- 
ing to the conditions of the problem, and its views are then drawn on the two planes 
which represent the planes of projection. 

The problems of this and the succeeding four plates are given mainly to illustrate 
the fundamental principles of orthographic projection. They are first drawn in isometric 
or cabinet projection, as the case may be, because it is thought that in this way the true 



1'ROBLEMS 



conception of the principles above referred to is more easily and quickly attained. In- 
cidentally further practice is also gained in the isometric and cubinit projections. 

At first it is easier to imagine the point, line, or object itself located in the angle 
between the two plane* of projection the views upon those planes will then follow. 
The first three problems of each of the five plates before mentioned will aid the imagina- 
tion in this. Eventually, however, the student will become accustomed to projection 
pure and simple, and will not need to go through this mental process. See Art. 64 (d). 

SPECIAL NOTES 

(a) Mark the two planes of projection HORIZONTAL PLANE and VERTICAL PLANE respective- 
ly, and their line of intersection GROUND LINE. Mark the top view and front view of the point 1, 
Ih and Iv respectively. Indicate that they are vietct of 1 by drawing two lines (of very ./me 
short dashes) to 1. The middle portion of each of these projecting lines may be omitted, only 
about ^" of each end being drawn. Ink in the ground line at least twice as heavy as any other 
line on the plate. Make the edges of the planes lighter than the other lines (projecting lines 
excepted). All similar lines on the plate should be of a uniform width. Ink in the given 
point or line with red ink. All other lines, including the view* on the planes, are black. 
Follow the above directions in the two succeeding plates also. 

(b) Arrange the given point and lines in the first three problems as symmetrically as pos- 
sible with respect to the edges of the planes, without conflicting with the given conditions. 

(c) Arrange each of the last three problems in the centre of its square, making the (/round 
line 3 in. long. Do not draw the outline of the planes of projection, simply the ground line. 

((?) If 2 is the end of the line 2-3 in II, then 2 coincides with 2h and 3h. Mark this point, 
which is also the top view of every point in the line 2-3, thus : 2 and 2-3h. 

OPTIONAL V 

1. Isometric drawing of a plain brick arch fireplace or similar object hav- 
ing a cylindrical surface. 

2. Cabinet drawing of the same object. Place the object so that the circles 
will be represented by ellipses. 



PLATE VI 
ORTHOGRAPHIC PROJECTION ILLUSTRATED BY ISOMETRIC PROJECTION 

Represent by means of isometric projection the following lines, together 
with the top view and front view of each on H and V respectively : 

1 (a). A straight line 1^2 2" long, parallel to both II and V, 2" below H 
and H" behind V. 

1 (ft). A straight line 1^2 2" long, parallel to both H and V, 1 J" below H 
and 2" behind V. 



2 (a). A straight line 3-4 2|" long, which makes an angle of 60 with II, 
is parallel to and 1 J" behind V. The upper end of the line is f " below II. 

2 (4). A straight line 3-4 3" long, which makes an angle of 60 with H, is 
parallel to and 1" behind V. The upper end of the line is in H. 

3 (a). A straight line 5-6 3" long, which makes an angle of 60 with V, is 
parallel to and 1" below II. The nearer end of the line is in V. 

3 (4). A straight line 5-0 2|" long, which makes an angle of 60 with V, is 
parallel to and If" below II. The nearer end of the line is f " behind V. 

Draw the top view and front view in true orthographic projection of : 

4 (a). The line 1^2 of 1 (a). 

4 (4). The line 1^2 of 1 (b). 

5 (a). The line 3^4 of 2 (). 

5 (4). The line 3^4 of 2 (4). 

6 (a). The line 5^6 of 3 (a). 
6 (6). The line 5^6 of 3 (b). 

NOTES PLATE VI 

Study Arts. 70-71. 

The general arrangement of the figures of this plate is similar to that of the pre- 
vious plate. There are only three red lines on the plate the given line in each of the 
first three problems. 

OPTIONAL VI 

Describe how to find the axes of the ellipses which represent circles in- 
scribed in the top and side faces of a cube in cabinet projection, and illustrate 
by a drawing. See Art. 56 (4). 



PLATE VII* 
ORTHOGRAPHIC AND CABINET ' PROJECTIONS 

1 (a). The top view of a line 1-2 is 2f" long and makes an angle of 45 
with the ground line, the nearer end being " behind the ground line; the 
front viw of the same line makes an angle of 30 with the ground line, the 
nearer end being ^" below the ground line. Find by means of orthographic 
projection the true length of the line 1-2. 

1 (b). Same as 1 (a), except the top view of the line makes an angle of 30 

* See Arts. 73 and 74. In abridged courses this plate may be given as an optional. 



8 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



with the ground line, while the angle which the front view makes with the 
ground line is 45. Length of the top view 2f ". 

2 (a). A line 3^4 is 2" long. Find its views on II and V in true or- 
thographic projection when the line itself makes an angle of 30 with H and 
of 45 with V. 

2 (b). Same as 2 (a), except that the line itself makes an angle of 45 with 
H and of 30 with V. 

Illustrate by means of cabinet projection the methods used in : 

3 (). Problem 1 (a). 

3 (b). Problem 1 (b). 

4 (a). Problem 2 (a). 
4 (b). Problem 2 (b). 

OPTIONAL VII 

If a line makes an angle of x with V and y with H, and ar+ y = 90, what 
angle will the plane in which the line lies make with H and V ? Illustrate by 
a drawing. 

PLATE VIII 

ORTHOGRAPHIC PROJECTION ILLUSTRATED BY CABINET PROJECTION 
Represent by means of cabinet projection the following solids, together 

with their top and front views on H and V respectively : 

1 (a). A square prism 2J" high ; side of base 1" long. The plane of the 

upper base is parallel to and f " below II. The plane of one side face makes 

an angle of 15 with V. The centre of the prism is 2" behind V. Let the 

nearest edge to V be a left-hand edge. (Note a.) 

1 (6). The prism of 1 (a) when one face is parallel to and 1J" behind V. 
The plane of the upper base is parallel to and f " below II. 

2 (a). A hexagonal pyramid 2" high; side of base 1" long; vertex over 
the centre of the base, 2" behind V. The plane of the base is parallel to and 

, 3^" below H ; two sides of the base are parallel to V. (Note b.) 

2 (b). The pyramid of 2 (a) in the same position, except no side of the base 
is parallel or perpendicular to V. (Note b.) 

3 (a). The prism of 1 (a) when the plane of a 2"xl" face is parallel to 
and 1J" below II, while another similar face is parallel to and 1" behind V. 
Show, in addition, an end view assuming the nearer end of the prism f " from 
the end plane. 



3 (b). A cylinder 2" long and 1J" in diameter, when the axis of the cylin- 
der is parallel to and 2" from both II and V. Show, in addition, an end view 
assuming the nearer end of the cylinder f ' from the end plane. 

Draw the top and front views in true orthographic projection of: 

4 (a). The prism of 1 (a). 

4 (6). The prism of 1 (b). 

5 (a). The pyramid of 2 (a). 

5 (b). The pyramid of 2 (6). 

6 (a). The prism of 3 (a). Draw also an end view. (Note a.) 

6 (6). The cylinder of 3 (b). Draw also an end view. (Notec.) 

NOTES PL ATE VIII 

Study Arts. 76 to 84 inclusive. 

From a point 4f" from both the lower and left-hand edges of each of the three 
upper squares, draw the three axes of cabinet projection. Construct upon these axes 
planes corresponding to the top and front faces of a 3J" cube, and let these planes rep- 
resent respectively H and V. First draw the solid itself in the angle thus formed, and 
then the top and front views of it on the planes representing II and V. 

The lines of the solid itself in each of the first three problems are drawn with red 
ink. All other lines on the plate, including those which represent the different views 
of the solids on the planes, are black. In orthographic projection certain edges are 
drawn heavier than others (Art. 128). 

Invisible edges are to be shown by broken lines of long dashes close togeth- 
er. Construction lines and projecting lines are very short, fine dashes (Arts. 32 a, 
326). 

The ground line for each of the problems iu true orthographic is 3|" long, and is 
drawn 3f " above the lower border line. 

Draw portions of each projecting line, and number corresponding points and views 
as 2, 2h, and 2v in each problem. 

(a) Before starting the top view, 1 (a), in cabinet projection, draw in pencil the top 
view of 4 () iu its proper place on the plate. This view will be a 1J" square, with 
one side at an angle of 15 with the ground line ; use the perpendiculars from ground 
line to the corners of this square as co-ordinates to find top view, 1 (a) (Art. 48 b). 
Whenever views cannot be drawn directly in cabinet or isometric projection, it will be 
found necessary to resort to a similar method of drawing a view in true orthographic 
projection first. 

(b) A common error is to forget to ink in the edges of the pyramid in the top view, 
2 (a), 2 ('), 5 (a), 5 (b). These edges, of course, are visible. 

(e) The clear space between the front and end views, 6 (a). 6 (6), is If". (Why ?) 
This makes it necessary to begin the front view T V from the left-hand side of the 
square. 



PROBLEMS 



OPTIONAL VIII 

1. Find the true shape and size of a triangular face of the pyramid of 
a (a), Plate VIII. Indicate clearly the method by broken lines in the 
drawing. 

2. Draw the top and front views of a hexagonal pyramid, a face of which is 
bounded by two sides, true length 3", and a third side 1" long. 

NOTE. No arithmetical calculation to be used in either problem. 



PLATE IX 

ORTHOGRAPHIC PROJECTION ILLUSTRATED BY CABINET PROJECTION 

Given an octagonal pyramid 2^" high ; side of octagon =J". Represent by 
means of cabinet projection this pyramid, together with its top and front views 
on II and V respectively, in each of the following positions : 

1 (a). When the plane of the base is parallel to and 3" below II. Vertex 
above the base. 

1 (/;). The same problem as 1 (a), substituting a heptagonal pyramid for 
the octagonal one of 1 (a). The heptagon can be inscribed in a circle 2" in 
diameter. 

2 (). When the plane of the base is parallel to and 3" behind V. Vertex 
in front of the base. 

2 (b). The same problem as 2 (a), substituting the heptagonal pyramid of 
1 (6) for the octagonal pyramid. 

3 (a). When the plane of the base is parallel to and -J" below H. Vertex 
below the base. 

3 (4). The same problem as 3 (a), substituting the heptagonal for the 
octagonal pyramid. 

4 (a). When the plane of the base is parallel to and " behind V. Vertex 
behind the base. 

4 (It). The same problem as 4 (a), substituting the heptagonal for the 
octagonal pyramid. 

Draw the top and front views in true orthographic projection of: 

5 (). The pyramid of 1 (a). 

5 (4). The pyramid of 1 (b). 

6 (a). The pyramid of 2 (a). 
6 (6), The pyramid of 2 (b). 



7 (). The pyramid of 3 (a). 

7 (b). The pyramid of 3 (b). 

8 (a). The pyramid of 4 (). 
8 (b). The pyramid of 4 (b). 

NOTES PLATE IX 

In the first four problems muke the planes of projection equal to the corresponding 
faces of a 3|" cube. *=f", y=lj". The axes of the pyramids are all If" from the 
planes to which they are parallel. 

Show all invisible edges unless they fall behind full lines. 

Draw the solids in red ink. 

Omit projecting lines and numbers in the true orthographic figures. Make ground 
line 7" long, 3J" above bottom border line. 

OPTIONAL IX 

Make a working drawing of 1 (a), Optional II. Give all necessary infor- 
mation and dimensions. See Chapter VIII. Show invisible edges by broken 
lines. 



PLATE X 

ORTHOGRAPHIC PROJECTION ILLUSTRATED BY ISOMETRIC PROJECTION 

Represent by means of isometric projection the following solids, together 
with the top, front, and end views of each on three planes of projection. 

1 (a). A hexagonal prism 2^" long ; side of hexagon J" long. The axis of 
the prism is parallel to and 1" from both II and V. The planes of two faces 
of the prism are each perpendicular to H. 

1 (b). The same problem as 1 (a), except the planes of two faces of the 
prism are each perpendicular to V. 

2 (a). A prism !-" square and 2-J-" long. The axis of the prism is parallel 
to and 1" from both H and V. Two faces of the prism are parallel to H. 
Through the centre of the prism, running lengthwise from end to end, there is 
a circular hole 1" in diameter. 

2 (b). A cylinder 1" in diameter and 2" long. The axis of the cylinder 
is parallel to and 1" from both H and V. Through the centre of the cylinder, 
running lengthwise from end to end, there is a hole j-" square. Two sides of 
the hole are parallel to H. 




10 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



Draw the top, front, and end views in true orthographic projection of : 
3 (a). The prism of 1 (a). 

3 (6). The prism of 1 (b). 

4 (a). The prism of 2 (a). 

4 (b). The cylinder of 2 (b). 

NOTES PLATE X 

In the first two figures make the planes of projection equal to the corresponding 
faces of a 3" cube. Draw the solids in red ink. 

Draw end views in true orthographic projection before drawing the problems in 
isometric projection. 

Show the hole in top and front views [2 (a), 2 (6), 4 (a), 4 (*)] by broken lines. 

OPTIONAL X 
Make a working drawing of 1 (c), Optional II. 



PLATE XI 

ORTHOGRAPHIC PROJECTION 

Draw the top, front, and side views in true orthographic projection of: 
1 (a). A hexagonal prism 3" high ; side of hexagon 1" long. The plane of 
the upper base is parallel to and " below II. No side face is parallel or per- 
pendicular to V. 

1 (b). A hexagonal pyramid 3" high ; side of hexagon 1" long. The plane 
of the base is parallel to and 3^" below H. No side of the base is parallel or 
perpendicular to V. Vertex is above the base. 

2 (a). A semi-cylinder, the front half of the original cylinder having been 
removed. The plane of the upper base is parallel to and " below II. The 
radius of the base is 1"; the height of the semi-cylinder is 3". 

2 (b). A semi-cone, the front half of the original cone having been removed. 
The plane of the base is parallel to and 3J" below II. The radius of the base 
is 1"; the distance of the vertex above the base is 3". 

3 (a). The frustum of the pyramid of 1 (b) when the pyramid is cut off by 
a plane parallel to and 2" above the base ; pyramid in the same position as in 1 (b). 

3 (b). A prism If" square and -3" high, having its upper base parallel to 
and J-" below II. Two side faces are perpendicular to V. In each of these 
side faces are two grooves, the centre lines of which correspond to the diag- 
onals of the face. Grooves are f " -wide and }" deep. 



4 (a). The frustum of the semi-cone of 2 (b) when the semi-cone is cut off 
by a plane parallel to and 2" above the base ; semi-cone in the same position as 
in 2 (6). 

4 (b). Three semi-cylinders, A, B, and C, the front half of each of the orig- 
inal cylinders having been removed. Each semi-cylinder is 1" high, and their 
radii are : for A 1 J", for B ", and for C ". C rests upon B, B upon A, and 
the plane of the base of A is parallel to and 3J" below II. The axes of all 
three cylinders are in the same straight line perpendicular to II. 

NOTES PLATE XI 

Let the solid in each problem be any convenient distance behind V. 

Show all invisible edges. The 2" is the perpendicular, not the slant height [3 (a), 
4 (a)]. The top view of the upper base of the frustum is obtained from the front 
view. 

OPTIONAL XI 

Make a working drawing of 1 (b), Optional II. 



PLATE XII 

ORTHOGRAPHIC PROJECTION 

Draw the top and front views in orthographic projection of the following 
solids described in previous plates : 
1 (a). The blocks of 3 (a), Plate II. 

1 (b). The blocks of 3 (b), Plate II. 

2 (a). The cube of 4 (a), Plate II. 

2 (b). The prism of 4 (b), Plate II. 

3 (a). The solid of 5 (a), Plate II.* 

3 (b). The cube of 5 (b), Plate II.* 

4 (a). The cylinders of 2 (a), Plate III.* 

4 (b). The prisms of 2 (6), Plate III.* 

5 (a). The block of 4 (a), Plate III.* 

5 (b). The block of 4 (b), Plate III.* 

6 (a). The cube of 6 (a), Plate III.* 
6 (b). The cube of 6 (b), Plate III.* 

* Problems marked* are to be drawn three-fourths full size; the other four problems are 
to be drawn full size. Arrange each problem in the centre of its square and omit ground lines. 
Choose the simplest position for each solid. 



PROBLEMS 



11 



OPTIONAL XII 
Make a working drawing of a carpenter's bench. 



PLATE XIII 

ORTHOGRAPHIC PROJECTION 1 ILLUSTRATED BY CABINET PROJECTION 

Given a prism 3" high and 1" square. Represent by means of cabinet pro- 
jection this square prism, together with its top and front views on H and V 
respectively when the prism is in the following positions: 

1 (). When the plane of the upper square base is parallel to and " below 
II ; centre of base 1" behind V. The plane of a side face makes an angle of 
30 with V. 

1 (b). When the plane of the front square base is parallel to and |" behind V ; 
centre of base 2" below II. The plane of a side face makes an angle of 30 with II. 

2 (a). Keeping the prism in the same position with respect to V that it is 
in in 1 (a), tip it up until the plane of the base makes an angle of 30 with H. 

2 (It). Keeping the prism in the same position with respect to H that it 
is in in 1 (b), tip it around until the plane of the base makes an angle of 30 
with V. 

3 (a). Keeping the prism in the same position with respect to H that it 
finally is in in 2 (a), revolve it until the top view of one of its longest edges 
makes an angle of 30 with the ground line. 

3 (b). Keeping the prism in the same position with respect to V that it 
finally is in in 2 (b), revolve it until the front view of one of its longest edges 
makes an angle of 30 with the ground line. 

Draw the top and front views in true orthographic projection of : 

4 (a.). The prism of 1 (a). 

4 (It). The prism of 1 (b). 

5 (a). The prism of 2 (a). 

5 (b). The prism of 2 (b). 

6 (a). The prism of 3 (a). 
6 (b). The prism of 3 (b). 

NOTES PLATE XIII 

Study Art. 85. 

For 4 (a), 5 (a), and 6 (a) the ground line is 4" above the lower border line ; for 4 (J), 
5 (b). and 6 (b) it is 3". 



In this plate draw the lower row or the last three problems first. The top views 
and front views thus obtained are then transferred to the cabinet planes of projection 
in the usual manner. These cahinet planes of projection correspond to the top and 
front faces of a 4" cube. Ink in a solid red, it views black. Ink in all construction 
and projecting lines, omitting, however, the centre portions in most cases. Show all 
invisible lines. 

OPTIONAL XIII 

Draw a ground plan of a house. Draw a second-story plan, also, if time 
permits. 

PLATE XIV 

ORTHOGRAPHIC PROJECTION 

Draw the top and front views in orthographic projection of : 

1 (a). A pentagonal prism 2|" high ; size of pentagon such that it can be 

inscribed in a 2" circle. The upper base is in H, with its centre 2" behind the 

ground line. 

1 (b). A pentagonal pyramid 3" high ; size of pentagon such that it can be 
inscribed in a 2" circle. The Vertex of the pyramid is in H ; plane of base par- 
allel to II ; axis of pyramid 2" behind V. 

2 (a). Keeping the prism in the same position with respect to V that it is 
in in 1 (a), tip it up until the plane of the base makes an angle of 30 with H. 

2 (b). Keeping the pyramid in the same position with respect to V that it is 
in in 1 (b), tip it up until the plane of the base makes an angle of 30 with H. 

3 (a). Keeping the prism in the same position with respect to H that it 
finally is in in 2 (a), revolve it until the top view of one of its longest edges 
makes an angle of 30 with the ground line. 

3 (b). Keeping the pyramid in the same position with respect to H that it 
finally is in in 2 (b), revolve it until the top view of its axis makes an angle of 
30 with the ground line. ' 

4 (a). The frustum of a hexagonal pyramid ; side of lower base 1" long ; 
side of upper base 1" long; perpendicular distance between the two bases is 
J". Plane of the lower base is parallel to and 2J" below H. On the centre ef 
the upper base rests a sphere 1" in diameter. 

4 (b). The blocks of 3 (a), Plate II., when the common axis of the three 
blocks is perpendicular to V, 1" below H. The plane of the nearest base is 
parallel to and J" behind V; two of its sides are parallel to H. 

5 (a). Keeping the two solids in the same position with respect to V that 



12 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



they are in in 4 (a), tip them until the plane of a base of the frustum makes 
an angle of 45 with II. 

5 (b). Keeping the blocks in the same position with respect to H that they 
are in in 4 (b), revolve them until the common axis makes an angle of 45 
with V. 

6 (a). Keeping the two solids in the same position with respect to H that 
they are in in 5 (a), revolve them until the top view of the line through the 
centres of the sphere and the hexagonal bases makes an angle of 45 with the 
ground line. 

6 (b). Keeping the blocks in the same position with respect to V that they 
finally are in in 5 (b), tip them down until the projection of the common axis 
on V makes an angle of 15 with the ground line. 

NOTES PLATE XIV 

Ground lines are in centre of rectangles for all problems except 4 (J), 5 (6), and 
6 (!f). For these problems ground lines are 3" from lower border line. 

OPTIONAL XIV 

A bridge pier is 12-0" high, 5'-0"x20'-0" on top, and has a slope on all 
sides of one in twelve. It is set on a skew of 30 with the roadway of the 
bridge. Show the top and front views of this pier when V is assumed at right 
angles to the roadway of the bridge. 



PLATE XV 

CURVES 

Construct an ellipse whose major and minor axes are respectively 4" and 2" 
long. 

1 (a). When the major axis is horizontal. 

1 (b). "When the major axis is vertical. 

Given a horizontal line 6" long. Through the two extremities of this line 
and a third point construct a parabola. 

2 (a). When the third point is 2" above the centre of the 6" line. 

2 (b). When the third point is 2" below the centre of the 6" line. 

3 (a). Draw two 45 lines each 6" long, bisecting each other at right angles 
in a point c. In the upper and lower angles thus formed construct a hyperbola, 



one branch in each angle, using a different method for each branch. Assume 
the vertices on a vertical line through c, the vertex of the upper branch 1" 
above c, the vertex of the lower branch 1" below c. 

3 (b). The same problem as 3 (a), except the branches of the hyperbola are 
drawn in the right and left hand angles respectively instead of the upper and 
lower angles. The vertices are on a horizontal line through c, 1" each side 
of c. 

Draw the top and front views in orthographic projection of : 

4 (a). A cone 3|" high ; diameter of base 2". The plane of the base is 
parallel to and 3f " below II. The axis of the cone is perpendicular to H and 
1" behind V ; vertex above the base. 

4 (b). The cone of 1 (a) when the plane of the base is parallel to and 3|" 
behind V. The axis of the cone is perpendicular to V and 1-J-" below II; ver- 
tex in front of the base. 

5 (a). Keeping the cone in the same position with respect to V that 
it is in in 4 (a), tip it until the plane of the base makes an angle of 30 
with H. 

5 (6). Keeping the cone in the same position with respect to H that 
it is in in 4 (b), revolve it until the plane of the base makes an angle of 30 
with V. 

6 (a). Keeping the cone in the same position with respect to II that it 
finally is in in 5 (a), revolve it until the projection of its axis on II makes an 
angle of 45 with the ground line. 

6 (b). Keeping the cone in the same position with respect to V that it 
finally is in in 5 (6), tip it until the projection of its axis on V makes an angle 
of 45 with the ground line. 

NOTES PLATE XV 

See Art. 45 for methods for drawing the curves. 

The ground lines for 4 (), 5 (a), and 6 (a) are 4" from the lower border line; for 
4 (6), 5 (J), and 6 (i) 3" from lower border line. 

Use two methods for 3 () or 3 (b.) Ink in all curves with the curve ruler (Art. 
22), except the ellipse in 5 (a) and 5 (b) and the larger ellipse in 6 (a) and 6 (b). These 
ellipses may be drawn with the compasses according to Art. 45. 

Ink in all axes in the upper row of figures, with a short dash and a long dash alter- 
nating (Art. 32 c). 

For method of finding axes of ellipses in 5 (a), 5 (b), 6 (a), and 6 (4), see Art. 87. 
Ink in the invisible portions of the ellipses in these figures. 



PKolJLIvMS 



13 



OPTIONAL XV 



Draw tbo top and front views of the cube of 4 (a), Plate II., in one of tlio 
most complicated positions with respect to II and V in which it can be placed 
i. e., no face parallel to II or V. 



PLATE XVI 
PLANE SECTIONS 

Represent by means of isometric projection the following solids, together 
with their top and front views on H and V respectively. 

1 (a). A cylinder 2" high ; 1-|" in diameter. The plane of the upper base 
is parallel to and J" below H. The axis of the cylinder is 1" behind V. The 
cylinder is cut by a plane parallel to V, -|" in front of the axis, and the part of 
the cylinder in front of the plane is removed. 

1 (b). A hexagonal prism 2" high; side of hexagon j$" long. The plane 
of the base is parallel to and " below II. The axis of the prism is 1" behind 
V. The prism is cut by a plane parallel to V, " in front of the axis, and the 
part of the prism in front of the plane is removed. 

2 (a). The cylinder of 1 (a) when its axis is parallel to and 1^" from both 
II and V. The cylinder is cut by a plane parallel to V, " in front of the axis, 
and the part of the cylinder in front of the plane is removed. Show, also, a 
view on the end plane. 

2 (b). The prism of 1 (6) when its axis is parallel to and 1" from both II 
and V. The prism is cut by a plane parallel to V, " in front of the axis, and 
the part of the prism in front of the axis is removed. Show, also, an end view. 

3 (n). A hexagonal pyramid 2" high ; side of hexagon -J-jj." long ; plane of 
base parallel to and 2|" below II ; vertex above base, 1" behind V. The pyra- 
mid is cut by a plane parallel to V, -fo" in front of the vertex, and the portion 
of the pyramid in front of the plane is removed. Assume two sides of the 
base parallel to V. 

3 (6). The same problem as 3 (a), except no side of the base of the pyramid 
is parallel or perpendicular to V. 

Draw the top and front views in true orthographic projection of: 

4 (a). The cylinder cut by a plane of 1 (a). 

4 (6). The prism cut by a plane of 1 (4). 

5 (a). The cylinder cut by a plane of 2 (a). Show, also, an end view. 



5 (b). The prism cut by a plane of 2 (b). Show, also, an end view. 

6 (a). The pyramid cut by a plane of 3 (a). 
6 (b). The pyramid cut by a plane of 3 (b). 

NOTES PLATE XVI 

Study Arts. 88-97. 

The planes of projection correspond to the faces of a 3" isometric cube in 1 (a), 
1 (J), 2 (), 2 (b), 3 (a), 3 (//). 

Section line the solid in red, the views in black (Art. 39). 

Represent the trace of the cutting plane in each problem by a dash and dot alter- 
nating (Art. 32 if), except where the plane cuts the solid. 

OPTIONAL XVI 

Make a working drawing of 1 (d) or 1 (e), Optional II., showing, in addition 
to the ordinary views, a section view. 



PLATE XVII 
PLANE SECTIONS 

Draw in orthographic projection the top and front views of : 

1 (a). A sphere 3" in diameter, having its centre If" from both H and V. 

It is cut by a plane parallel to V, " in front of the centre of the sphere, and 

the portion of the sphere in front of the plane is removed. 

1 (b). Same as 1 (a), except the cutting plane is parallel to H, |" above the 
centre of the sphere, and the portion of the sphere above the plane is removed. 

2 (a). A hollow 3" cube, with an open hole 1" square in the centre of each 
face. The distance between the inner and outer surfaces is -f^". The plane 
of the upper face is parallel to and ^" below II ; the plane of the front face is 
" behind V. The cube is cut by a plane through its centre, parallel to V. 

2 (b). The same as 2 (a), except the cutting plane passes through the centre 
of the cube parallel to H instead of V. 

3 (a). A cylinder 3" high, 2" in diameter ; plane of lower base parallel to 
and 34/' below H ; axis 1" behind V. The cylinder is cut by a plane perpen- 
dicular to V, and making an angle of 45 with H. The portion of the cylinder 
above the cutting plane is removed. Assume the cylinder to be cut 2" up the 
axis. (Show, also, true size of section cut.) 

3 (b). A hollow hexagonal prism 3" high ; side of larger hexagon 1" long; 



14 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



perpendicular distance between the inner and outer surfaces is f"; plane of 
the lower base is parallel to and 3f below H ; axis of the prism 1" behind 
V. The prism is cut 2" up its axis by a plane perpendicular to V, and making 
an angle of 45 with H. The portion of the prism above the cutting plane is 
removed. (Show, also, true size of section cut.) 

4 (a). A hollow hexagonal pyramid 3" long from base to vertex ; side of 
larger hexagon 1" long; perpendicular distance between the inner and outer 
surfaces is " ; axis of the pyramid parallel to and 1" from both H and V; 
no side of the base parallel or perpendicular to H. The pyramid is cut by a 
plane parallel to V and " in front of the axis. The portion of the pyramid in 
front of the plane is removed. 

4 (b). The same as 4 (a), except the cutting plane is parallel to H 
and " above the axis. The portion of the* pyramid above the plane is 
removed. 

5 (a). The pyramid of 4 (a) when the plane of its base is parallel to and 
3J" below H ; axis 1" behind V ; no side of the base is parallel or perpendic- 
ular to V. The pyramid is cut by a plane through its axis perpendicular to H, 
and making an angle of 30 with V. The portion of the pyramid in front of 
the cutting plane is removed. 

5 (b). The pyramid of 5 (a) in the same position as in 5 (a). The cutting 
plane passes through the vertex of the pyramid and intersects the plane of the 
base in a line parallel to V, " in front of the centre of the base. The portion 
of the pyramid in front of the cutting plane is removed. 

6 (a). The sphere of 1 (a) in the same position as in 1 (a). The cutting 
plane is perpendicular to H and makes an angle of 30 with V. The nearest 
distance from the centre of the sphere to the cutting plane is ". 

6 (b). The same as 6 (a), except the cutting plane is perpendicular to V and 
makes an angle of 30 with H. The nearest distance from the centre of the 
sphere to the cutting plane is f ". 



OPTIONAL XVII 

A prism 2-J-" square has its base parallel to H. Find the true shape of the 
section cut from it by any plane (except a profile plane) at an angle with H 
andV. 



PLATE XVIII 

CONIC SECTIONS* 

Given : A cone 4" high ; diameter of base 3" ; plane of base parallel to and 
4^" below H ; vertex above the base ; axis of the cone 3" behind V. Draw 
the top and front views in orthographic projection of this cone when cut by : 

1 (a). A plane parallel to V and " in front of the axis. 

2 (a). A plane perpendicular to V and making an angle of 45 with H. 
The plane cuts the axis of the cone If" from the base. Show, also, the true 
shape of the section cut from the cone. 

3 (a). A plane perpendicular to V and parallel to an extreme side element 
of the cone. The plane cuts the axis of the cone 2J" from the* base. Show, 
also, the true shape of the section cut from the cone. 

Given : A cone 4" high ; diameter of base 3" ; plane of base parallel to and 
4" behind V ; vertex in front of the base ; axis of the cone 3" below H. 
Draw the top and front views in orthographic projection of this cone when 
cut by : 

1 (b). A plane parallel to II and $" above the axis. 

2 (b). A plane perpendicular to II and making an angle of 45 with V. 
The plane cuts the axis of the cone If" from the base. Show, also, the true 
shape of the section cut from the cone. 

3 (b), A plane perpendicular to H and parallel to an extreme side element 
of the cone. The plane cuts the axis of the cone 2" from the base. Show, 
also, the true shape of the section cut from the cone. 

OPTIONAL XVIII 
Draw a plate of line-shading similar to that shown on page 105. 



PLATE XIX 

INTERSECTION OF THE SURFACES OF SOLIDS t 

Show by means of isometric projection the following solids, together with 
their top and front views on H and V respectively. 

1 (a). Two intersecting cylinders whose axes bisect each other at right 

* Study Arts. 98 (a), (b), (c). t Stud )' Arts - 12-104. 



PROBLEMS 



15 



angles. One cylinder with its upper base in H is 2" in diameter, the other, 
witli its axis parallel to 11 and V, is 2V in diameter. Each cylinder is 5" long. 
The axis of the vertical cylinder is 3" behind V. (Let II and V correspond to 
the top and front faces of a 6" isometric cube.) 

1 (/<). The same problem as 1 (), except the larger cylinder is vertical and 
the smaller cylinder horizontal. 

Draw the top and front views in true orthographic projection of: 

2 ((/). The cylinders as they are in 1 (a). 
2 (A). The cylinders as they are in 1 (b). 



NOTES PLATE XX 

Study Arts. 105, 107 and 109, 110. 

For this plate divide the space within the border line into four spaces each 
14"x5J" . 

OPTIONAL XX (to be drawn after Plate XXI) 

Make out of card -board the two intersecting cylinders of 3 (a), Plate 
XXI. 



OPTIONAL XIX 
Make out of card-board the two intersecting cylinders of Plate XIX. 



PLATE XX 

INTERSECTION OF THE SURFACES OF SOLIDS 

Draw the top and front views in true orthographic projection of : 
1 (a). The intersection of a sphere 4" in diameter, with its centre 2V from 
II and 3J" from V, by a cylinder 5" high and 1 " in diameter. Upper base of 
the cylinder is in 11, with its centre on a 45 line through the top view of the 
centre of the sphere IV from it. 

1 (b). The same problem as 1 (a), substituting a hexagonal prism 5" high, 
side of hexagon J" long, for the cylinder given in 1 (a). 

2 (a). Develop one end of the cylinder of 1 (a). 

2 (b). Develop one end of the prism of 1 (6). 

Draw the top and front views in true orthographic projection of : 

3 (). The intersection of a cylinder and hexagonal prism whose axes 
bisect each other at right angles. The cylinder is 5" long and 2V in diam- 
eter ; its upper base is in II; its axis is 3V behind V. The axis of the prism 
is parallel to both II and V; a side of the hexagon is 1" long; length of 
prism 5". 

3 (b). Same as 3 (a), except the cylinder is 2" in diameter, while the length 
of a side of the hexagon for the prism is 1 V- 

4 (a). Develop one end of the prism of 3 (a). 

4 (b). Develop one end of the cylinder of 3 (4). 



PLATE XXI* 

INTERSECTION OF THE SURFACES OF SOLIDS 

Draw the top and front views in orthographic projection of: 
1 (a). The intersection of a cone and a cylinder. The cone is 4" high and 
the diameter of its base is 3" ; the plane of its base is parallel to and 4V below 
H ; vertex above the base. The cylinder is 2" in diameter and 4" long. The 
axis of the cylinder is parallel to both II and V, and intersects the axis of the 
cone 1 V from the base of the cone. 

1 (b). Same as 1 (a), except the axis of the cylinder intersects the axis of 
the cone If" from the base of the cone, 

2 (a). Develop the cone of 1 (a). 

2 (b). Develop the lower part of the cone of 1 (b). 

Draw the top and front views -in orthographic projection of : 

3 (a). The intersection of a vertical by an oblique cylinder. The vertical 
cylinder is 2V in diameter and 4" high, with its tipper base parallel to and V 
below H. The oblique cylinder is 4" long and 2" in diameter, with its axis 
parallel to V, but making an angle of 15 with H. The axes of the two cylin- 
ders bisect each other. 

3 (b). The same as 3 (a), except the diameter of the vertical cylinder is 2", 
while that of the oblique cylinder is 2". 

NOTES PLATE XXI 

Study Art. 106. 

Divide the plate into three spaces each 14" x 7". 

* This plate may be omitted in abridged courses. 



16 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



OPTIONAL XXI 

A 3" pipe passes through a hollow box 12" x 12"xl2". Sides of box 1" 
thick. The centre of the pipe is 4" from the left-hand and lower sides of the 
front face of the box and 4" from the right-hand and upper edges of the back 
face. Make a working-drawing of the box, showing the shape of holes in the 
sides for the pipe to pass through. 



Do not ink in the outline of the shadow. 
Put on the tint before inking. 

Shade the parts of the different views in shadow a lighter tint than that used for 
the shadows on H. 

OPTIONAL XXII 

Find the isometric shadows of the solids of 4 (a), Plate II., and 5 (a), 
Plate III. 



PLATE XXII 

SHADOWS 

Find the shadow cast upon II by : 

1 (a). The square prism of 4 (a), Plate VIII. Assume the lower base in H ; 
the front edge is 6J" in front of V ; the right-hand side face makes an angle 
of 60 with V. 

1 (b). A square prism 2J" high ; side of base 1-J-". Base in H. Front face 
to and 6" in front of V. 

2 (a). The octagonal pyramid of 1 (a), Plate IX., when its base is parallel 
to and J" above H ; axis 5^" in front of V ; vertex above the base. 

2 (b). A heptagonal pyramid 2^" high ; base inscribed in a circle 2" in 
diameter. Plane of base parallel to and 1" above H. Axis 5" in front of V. 

3 (a). The semi-cylinder of 2 (a), Plate XL, when its lower base is in H 
and the axis 5J-" in front of V. 

3 (6). The semi-cone of 2 (4), Plate XL, when the base is parallel to and 1" 
above H. Axis of cone 6" in front of V. 

NOTES PLATE XXII 

Study Arts. 112-120, and Art. 40. 

Divide the space within the border line into three 14" x7" rectangles. 

The distance from the left-hand side of the rectangle to a point in the top view is : 

For Fig. 1 (a) about 2 T y to the top view of the front edge of prism. 

For Fig. 1 (b) about 1 J" to left-hand front corner of base. 

For Fig. 2 (a) about 2}^" to centre of octagon. 

For Fig. 2 (b) about 2" to centre of heptagon. 

For Fig. 3 (a) about 2" to centre of semi-circle. 

For Fig. 3 (b) about 2" to centre of semi-circle. 
The ground line for each figure is 5" below the top of the rectangle. 



PLATE XXIII 

SHADOWS 

Find the shadow cast upon H by : 

1 (a). The blocks of 3 (a), Plate II., when the base of the lower block is 
in H. Assume the front side of this base parallel to and 6J" in front of V. 

1 (6). A square prism 2" high ; side of base 1". Front face parallel to 
and 7" in front of V. Plane of base makes an angle of 30 with H. The 
lowest edge is in H. 

2 (a). The frustum and block of 5 (a), Plate II., when the lower base of 
the block is in H. Assume the front side of this base parallel to and 6i" in 
front of V. 

2 (b). On the top of a 1J" cube is a block 1 J" wide, 1" high, 3J" long. 
The centre of the block is over the centre of the cube. The plane of the left- 
hand front faces of block and cube makes an angle of 30 with V. The front 
edge of block is 7" in front of V. Base of cube in II. 

3 (a). Same as 3 (b) below, substituting cylinder 2" and 1" in diameter re- 
spectively for the corresponding hexagonal prisms. Front face of square block 
6" in front of V. 

3 (b). In the centre of the upper face of a block 4" square and " high 
stands a hexagonal prism 1" high, with two faces perpendicular to V. Length 
of side 1". In the centre of the upper base of this prism stands a second hex- 
agonal prism 1" high, with two sides perpendicular to V; length of side ". 
The front face of the square block is parallel to and 7" in front of V. Base of 
square block in H. 

NOTES PLATE XXIII 

The ground lines aud the spaces for the figures are the same as for the preceding 



PROBLEMS 



17 



plate. The distance from the left-hand side of a rectangle to a point in the top view 
of the corresponding figure is : 

For Fig. 1 () about 1" to left-hand front corner of lowest block. 

For Fig. 1 (b) about 2|" to lowest corner, front ri, w. 

For Fig. 3 (a) about }J" to left-hand front corner of lower block. 

For Fig. 3 (!>) about 3\" to front corner of upper block. 

For Fig. 3 (</) about " to left-hand front corner of square block. 

For Fig. 3 (f/) about {f " to left-hand front corner of square block. 
In 3 () and 3 (6) the shadow of the middle solid falls upon the upper face of the 
square block instead of on H. 

OPTIONAL XXIII 

1. A vertical cylinder 2V in diameter and 3V high stands with its base in 
II. Tint the shadow on 11 and shade the cylinder by the graded tints. See 
Art. 41. Let the cylinder be such a distance from V that a small portion of its 
shadow falls on V. 

2. Same as the above, except draw cylinder in isometric, tint isometric 
shadow. Shade cylinder with graded shading. 



PLATE XXIV 

PERSPECTIVE 

Make a perspective drawing of : 

I (a). A 2" square plate, 1 V square hole in centre, in picture plane, edges 
vertical. Two similar plates exactly behind it, with 4" space between. x=\^", 
y = 1 V. (Notes a and b.) 

1 (b). A 2V X 3" rectangular plate, with l"xlVhole placed symmetrically 
in the centre. 3" side vertical. Place in picture plane, with two similar plates 
directly behind, 4" apart. x= IV, y = lV. (Notes a and b.) 

2 (a). A 3" square plate with 2" square hole in centre. It is horizontal, 
with one edge in the picture plane. Two others behind it, 3V apart. ar=l|-", 
y=lV. (Note c.) 

2 (b). The plate of 1 (b) with its plane horizontal and the 3" edge in the 
picture plane. Two others behind it and 2^" apart. (Note d.) 

3 (a). A 3" square plate, IV square hole in centre. Perpendicular to the 
picture plane. One edge vertical and lies in the picture plane. Two others 
behind it, with 3" space between them. # = 5", y=l". 

3 (b). The plate of 1 (b) with 3" edge vertical and in the picture plane. 
2 



Plate perpendicular to the picture plane, with two others behind it, 2V apart 
*=6f',y=l". 

4 (). A 2V cube, face in picture plane, edges vertical. Another cube be- 
hind this, 2" space between. j = lV, y=lV- 

4 (b). A square prism 3" high, side of base 2". 2"x3" face in the picture 
plane, with 3" edge vertical. Another prism exactly behind, 2" space between. 
*=ll,y = l". 

5 (a). A square prism " high, side of base 3V, with 2" square hole in 
centre of square face.' 3V xf" face in the picture plane. " edge vertical. 
Two others behind it, with 3V space between them. z=lf", y=lV (Notee.) 

5 (b). Same problem as 5 (a), except that there is no square hole; instead, rec- 
tangular notches 2" x " X f " are cut from the edges of the block front and rear. 

6 (a). Square pyramid 3" high, side of base 2". Axis vertical. One edge 
of base horizontal and in .the picture plane. Two others behind, with basea 
spaced 2" apart, x4", y=lV. (Note/.) 

6 (b). Square pyramid 3" high, side of base 2V. Axis vertical. Base 
horizontal and one edge in the picture plane. Second pyramid directly behind, 
with 2V space between. x=3", y=lV. (Note/.) 

NOTES PLATE XX I V. 

Before beginning this plate read Chapter VII., Arts. 130-140, 143. 

(a) The first three problems have the horizon 1J" below border line. Take S in 
the middle of the horizon, and same for all three problems. S to D = 16", and use it 
one-half size. Ink in visible outlines of objects heavy, construction lines in fine dots. 
The last three problems have horizon 1" below the centre of the sheet. S to D= 16", 
and S put in centre of the horizon. 

Remember that nil measurements must be made in the picture plane. 

(b) In 1 (<;) and 1 (b) the plate in the picture plane is drawn in its actual outline. 
The other figures appear smaller, since their corners lie on lines converging towards S. 

(c) In 3 (a) draw all the 3^" square plates, first leaving out the square hole in the 
centre. Then take 3" in the middle of the front edge and join to S. The intersection 
of these lines with the diagonals of the squares gives the 2" square hole. 

Art. 143 on equidistant spacing applies well to locating the corners of the larsre 
squares. 

(d) In 2 (b) the holes, 1" x 1J", in the centre of each plate must be located by meas- 
urement H" on the front, edge, 1" on the side edge. 

(e) 5 (a) is the same as 2 (a), except that the solid has thickness. Show the visible 
edges only. 

(/) In 6 (a) and 6 (b) locate the vertex from intersection of the diagonals of the base. 
The height, however, must be measured in the picture plate. 



18 



AX IXTRODUCTORY COURSE IX MECHANICAL DRAWIXG 



OPTIONAL XXIV 

A cone 4" in diameter at base and 5" high stands in such a position that a 
small portion of its shadow falls on a cylinder 3" in diameter and 5" high. 
Show all shadows, and shade the cylinder and cone with graded shading. 



PLATE XXV 
PERSPECTIVE 

Make a perspective drawing of : 
1 (a). The block of 3 (a), Plate III. 

1 (6). The blocks of 3 (b), Plate II. 

2 (a). The block of 4 (a), Plate III. 

2 (b). The block' of 4 '(b), Plate III. 

3 (a). The block and frustum of 5 (a), Plate III. 

3 (b). The two lower blocks of 5 (b), Plate III. 

4 (a). The block of 5 (a), Plate II. 
4 (6). The cube of 4 (a), Plate II. 

NOTES PLATE XXV 

The rectangle for each problem is 7" x 10J". 

For 1 (a), 1 (b), 2 (a), and 2 (b) the point of sight is \" below the upper border line on 
the line between the two upper rectangles. 

For 3 (a), 3 (b), 4 (a), and 4 (*) the point of sight is 7" below the upper border line 
on the line between the two lower rectangles. 

In 1 (b) assume a 2"xl" face of middle block parallel to and \" behind the picture 
plane with a 2" edge horizontal. This makes two vertical 1" edges 3J" apart in the 
picture plane. 

In 3 (a) assume a 4" x^" face of lower block in picture plane. 

In 3 (b) assume two faces of lower block perpendicular to picture plane with the 
front vertical edge of the block in the picture plane. 

In 4 (a) assume the smaller end of the block in the picture plane. 

The distance of the eye from the paper is 14" for all problems. 

1 (), r=2", y=\". 1 (6), x=2%", y=l" (to lower end of left-hand vertical 1" 
edge). 

2 (a), z=4J.", y=\". 2 (b), x-^', y-l". 



3 (a), .T=2J-", y=\". 3 (*), *=2f", yl\" (to lower end of vertical edge in picture 
plane). 

4 (a), z=5", y=H". 4 (b), a;=5f", y=H". 

x and y are to the lower left-hand corner of face in picture plane, unless other- 
wise noted. 

OPTIONAL XXV 

Make perspective drawings of 4 (a), Plate XXIV., and 3 (a), Plate III., 
when no face is parallel to or in the picture plane. 



PLATE XXVI 
PERSPECTIVE 

Make a perspective drawing of : 

1 (a). The frustum of a cone, 1 (a), Plate IV. 

1 (b). The cylinders, 1 (6), Plate IV. 

2 (a). A cylinder 3" in diameter, 3" high. Axis vertical. 

2 (b). A cylinder 3" in diameter, 3" long. Axis horizontal. 

3 (a). The cube, 3 (a), Plate IV. 
3 (b). The cube, 3 (b), Plate IV. 

NOTES PLATE XXVI 

Study Art, 142. 

Divide the plate into three 14" x 7" rectangles. 

The point of sight for all problems is 5" above the centre of the sheet, or 3" below 
top of centre rectangle. 

1 (a), x2", y=4|", to left-hand front corner of square in which lower base is in- 
scribed. 

1 (b), x=2", y4^", to left-hand front corner of square in which lowest base is in- 
scribed. 

2 (a) and 2 (b). Cylinder is directly in front of point of sight, about 5" from lower 
border line. Front element in picture plane. 

3 (a) and 3 (b), x=%", ?/=4f", to lower left-hand corner of face in picture plane. 
Distance of eye from paper 16" for all problems. 

OPTIONAL XXVI 
Make a perspective drawing of a house. 



CHAPTER I 

THE SELECTION OF THE OUTFIT 




1. IT is important that the student of drawing should have a 
good outfit ; a poor one prevents him from doing his best work, and is 
a constant source of annoyance. The beginner will be well repaid for 
inn/ precautions he may take resulting in the selection of satisfactory 
//, >,/,/;,,,/ instruments <iml materials.* 

An engineering student should be particularly careful in selecting 
his drawing instruments, since, with proper care, they can be used for 
many years. 

2. It is well to purchase the outfit of some reliable dealer, where 
any part of it may be readily exchanged if found defective or in any 
way unsatisfactory. A list' of instruments and materials needed by 
the draftsman is here given. The list is purposely made small. The 
draftsman can, from time to time, make such additions to this collec- 
tion as are required by his work, he being better able to select wisely 
for himself as time goes on. 

LIST OF INSTRUMENTS AND MATERIALS 

1 Drawing-board (24" x 17"). 

1 Set of Drawing Instruments, including Ruling-pen, Compasses with Pen, 
Pencil, and Lengthening Bar, with extra IIIIIIIIII1I Leads. 

1 T-square, 24" blade (see Fig. 3, page 23). 

1 45 Triangle, 9 inch (see Fig. 3). 

1 30x60 Trianirl.', 11 inch (see Fig. 3). 

1 iL'-inoh Flat Scale, divided into sixteenths. 

* When possible the student should intrust the selection of his outfit to a competent 
judge of drawing instruments and materials. 



r Semi-circular Protractor, 5 inch. 

1 Curve, similar to K. & E. Rubber No. 26. 

1 Drawing-pencil, HHHHHH. 




FIG. 1 



1 Erasing Rubber. 
7- 6s Thumb-tacks. 






1 Pen-holder, Writing-pens (Nos. 404 and 303 Gillott's), and Pen-wiper. 

1 Bottle Liquid India-ink ; 1 Bottle Red Drawing-ink. / | - 

1 Pencil-pointer (fine flat file or sand-paper). 

White Drawing-paper (number and size of sheets depending upon the work to 
be done). For this course at least twenty-four sheets similar to Keuffel 
& Esscr's "Normal Paper," 22 inches long and 15 inches wide. 



20 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



The following list of materials for tinting not needed at the outset is 
placed here for future reference : 

1 Brush, size of K. fc E. No. 3121-14 or No. 7 Devoe. 

Stick of India-ink. 

1 Water-glass 2- inches in diameter. 

1 Cabinet Saucer, or Nest of Saucers, 3^ inches in diameter. 

1 Small Sponge. 

Paper especially adapted to tinting. 

3. The Compasses. Compasses with the needle-point leg non- 
it, taehable, the pen or pencil-holder forming the other leg, are prefer- 
able. This does not mean that either leg is without a joint, for such 
compasses, the legs of which cannot be bent (see Fig. 11, page 27), are 
of little value. Test the compasses for alignment by bending both 
legs, bringing the extremities together; they should meet perfectly. 
Undue effort should not be required to remove the shank of the pen- 
cil-holder from the socket, and the pen should be as easily fitted in its 
place. All shanks, however, should fit the sockets accurately, too 
loose joints being as bad as too tight ones. The needle-poin-t should 
have a shoulder to prevent a large hole being made in the paper. 
The pen which belongs to the compasses has many points in common 
with the ruling-pen (see Art. 4). The best instruments are of rolled 
metal (usually German-silver), while the cheaper kind are of cast metal. 
The latter usually have a more polished or glossy finish than the former, 
and are easily recognized by one familiar with drawing instruments. 
The quality of the rolled metal cannot be determined by inspection ; 
the reputation of the maker is the best guarantee of its excellence. 

In addition to the instruments previously mentioned, the drafts- 
man will probably need sooner or later a pair of hair-spring dividers, 
a pair of bow pen-compasses, a pair of bow pencil-compasses, and an 
extra inking-pen. When buying the instruments required at the start, 
it is well to have them put in a case large enough to contain these 
additions should they ever be made. 

At present prices (1897) a pair of compasses, with attachments (pen, pencil, 
and lengthening bar), good enough for ordinary work, can be bought for $3.00. 
A first-class set of the same number of pieces costs about $7.50. 



4. Ruling-pen. It is poor economy to buy a second-class ruling- 
pen a good one is absolutely necessary. A poor ruling-pen belongs 
in the same category with a writing-pen that scratches or a pencil 
which cannot be made to mark. If cheap instruments are bought, 
let the dealer replace the ruling-pen belonging to the set by a first- 
class pen. The difference in cost is not to be compared with the ad- 
ditional comfort to be derived from the use of a good pen. The first 
test of a pen is its ability to rule clear, full lines of different widths. 
No pen will do this unless its nibs are of even length and moderately 
sharp. Pens with ivory or bone handles are usually of inferior 
grade, and if dropped break easily. Blades ending in a rounded point 
are preferable to those having a narrow sharp one. The upper 
blade should have the thin spring back of the set-screw. The pen 
whose upper blade is hinged for the purpose of cleaning is going 
out of use. One is made, however, by Alteneder, which can be 
opened, cleaned, and closed again without changing the width of 
line; this pen is highly recommended. Its price is more than that 
of an ordinar\ r pen, however, and makes it a luxury rather than a 
necessity. 

An ordinary inking-pen of medium size costs from $1.40 to $1.90. 

5. Care of Instruments. Without proper care the best of in- 
struments are quickly spoiled. The directions are simple /-.// tit, HI 
clean and dry. Ink xfioultl not le allowed to dry in the pen, and all 
pieces should be wiped with cloth or chamois after using. It will 
be necessary to sharpen the pens occasionally, and every draftsman 
should possess a thin oil-stone for this purpose. Screw the nibs close 
together, and draw the pen across the stone a few times precisely as 
if drawing lines upon it, but changing the inclination of the pen from 
one side of the vertical to the other, so as to keep a rounded point. 
This will make the nibs of equal length, but dull. Unscrew the pen 
and sharpen each nib separately by rubbing its <>n1< r side on the 
stone, taking care to hold the pen at a smnR angle with the horizon- 
tal. The burr on the inside of the nibs may be removed by a stroke 
or two on the stone or with a fine flat lile. 



TIIK SKLKCTIOX OF THE Ol'TI-IT 



31 



6. T-Square. The chief requisites in a good T-square are : (1) 
That the blade be securely fastened to the head ; (2) that the inside 
edge of the head be perfectly straight ; C-!) that the upper or ruling 
edge of the blade be perfectly smooth and straight, free from all 
nicks or rough places. The blade is more apt to remain true if the 
grain of the wood is parallel to the ruling edge. 

A wooden T-square with a blade 24 inches long can IK- bought for about 25 
cents. One with ebony or celluloid edges costs from 75 cents to si. 50. 

7. Triangles. Wooden triangles are usually inaccurate. Rubber 
or celluloid triangles are much to be preferred. Any triangle is liable 
to warp, but it should at least be straight when bought. Celluloid 
triangles warp more easily than rubber ones, but attract less dust, 
making it easier to keep the drawing clean. There is some advan- 
ta^e, also, in working with transparent triangles. On the whole, cel- 
luloid triangles are perhaps the best ; they should have, however, a 
thickness of nearly a sixteenth of an inch, because of the tendency 
to warp if thin. Since the triangles are used for ruling, all edges 
should be smooth and straight. The right angles may be tested for 
accuracy by placing one side against the T-square and drawing a ver- 
tical line (see Fig. 3, page 23). Turn the triangle over, placing the 
same side against the T-square, and if the angle is not a right angle 
the vertical side will not coincide with the vertical line. Similar tests 
for the 45, 30, and 60 will suggest themselves to any one familiar 
with elementary principles of geometry. 

Wooden triangles cost about 25 cents each. Celluloid and rubber triangles 
of the size recommended cost from 50 cents to 90 cents each. 

8. Scale. A 12-inch flat scale with bevel edges will answer every 
purpose. It will be found convenient to have one edge divided into 
sixteenths of an inch, the other edge into tenths of an inch. In some 
classes of work triangular scales are used. The usual form is the 
"Architect's" triangular boxwood scale, 12 inches long, with divisions 

&' A, i, i, ib i. f !< H. and 3 inches to the foot - 

A flat scale costs about 50 cents; a triangular scale about 1.00. 



9. Inks. For a certain class of work draftsmen often prefer to 
make their own ink from Chinese stick-ink. For ordinary work pre- 
pared inks sold in bottles having some device in the stopper for till- 
ing the pen will answer every purpose. The ink should be absolutely 
black and opaque, and adhere to the paper when dry, even if rubbed 
over; should flow readily, dry quickly, and retain these properties for 
a reasonable length of time after the bottle is opened. Water-proof 
inks are preferable. Iliggins's water-proof inks are recommended. 

Cost, 25 cents per bottle. 

10. Drawing-boards. At most schools and colleges boards are 
loaned to the students. The ends should be straight and true to 
allow perfect contact with the head of the T-square. It is not nec- 
essary that the corners of the board should be exact right angles, the 
T-square being used on one edge of the board only. Warping should 
be guarded against by cleats or some other device. The top of the 
board should be one smooth plane. 

A drawing-board 18 in. x24 in. costs from 50 cents to 75 cents. 

11. Drawing-paper. The surface of the drawing-paper should 
be such that a clear, sharp ink-line of any width can be drawn upon it ; 
it should stand a reasonable amount of erasing without being destroy- 
ed or rendered unfit for further inking. Keutfel <k Esser's "Normal 
Paper" meets these requirements, and for ordinary work is as satis- 
factory as the more expensive papers. 

Cost of sheets 22 in. x 15 in. about 50 cents per dozen. 

12. Miscellaneous. A curve of wood, rubber, or celluloid, sim- 
ilar to the one shown in Fig. 1, is recommended. Cost, from 20 cents to 
45 cents. A small metal protractor, of about 2-inch outside radius, 
costs 50 cents. A horn protractor costs 25 cents. The pencil should 
be very hard (HHHIIHII); cost, 10 cents. The extra leads for the 
compasses should he equally Jun-d. A fine flat file is the best pencil- 
pointer. The pin of the thumb-tack should not be over T 3 ^ in. long. 



2.2 AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 

The " multiplex" erasing rubber and "Davidson's Velvet " rubber are is not advisable to go. Materials and instruments can be bought 

recommended. cheaper, but they are as a rule unsatisfactory. It may be nec- 

13. Summary: Estimated Cost of Outfit. In the following essary, however, in some cases to buy a less costly outfit than is here 
estimate the minimum cost has been fixed at the point below which it given : 

Miiiiniiitii. Sfaximum. 

Compasses, with attachments $3.00 87.50 

Ruling-pen 1.40 1.90 

T-sqnare 25 1.50 

Triangles 50 1.75 

Curve 20 45 

Scale 50 1.00 

Protractor 25 50 

Inks (black and red) 50 50 

Paper (24 sheets 22" x 15") 1.00 1.00 . 

Miscellaneous . 40 50 



Total $8.00 $16.60 

To the above list may be added materials for tinting, costing 
about 75 cents, and a drawing-board, in case one is not furnished by 
the school, costing from 50 cents to 75 cents. 



CHAPTER II 
THE USE OF THE DRAWING INSTRUMENTS* 



14. The Pencil. Pencil lines should be as fine and light as pos- 
sible and still be clearly visible. Bearing on hard with the pencil 
^ will cut the paper und leave a mark 

which cannot be erased. The pencil 
should be sharpened to a thin wedge- 
shaped lead at one end (see Fig. 2), and a 
xli<n'i> round-pointed lead at the other end. 
The flat lead is used for drawing lines; 
the round lead for marking points, letter- 
ing the drawing, and all similar work. 
Lines are drawn with the flat side of the 
pencil lead pressed lightly against the 
ruling -edge, the pencil itself being held 
nearly vertical. Lines should be so close 
to the ruling-edge that they are scarcely 
visible until the edge is moved away. To insure this, it may be nec- 
essary to incline the pencil-top slightly outward, thus bringing the 

* In this chapter the intention 1ms been not to give a single unimportant direction, 
nor one not based upon the common experience of the best draftsmen. The begin- 
ner is urged to follow the directions as closely as possible, even though Ilie reason 
for doing a thing in a certain way may not sit first always be apparent. Habits formed 
at the start are not easily changed. Extra precautions are therefore necessary on the 
part of instructor and student that the latter may acquire early the shortest and best 
methods of work. 

The student is not expected to read this chapter from beginning to end, but to 
study each article as it becomes necessary for progress in the work. The best results 
will be obtained by rereading the most important articles, such as that on the use of 
the ruling-pen, several times during the course. 



FIG. 2 
Two views of the wedge shaped lead 



lead in contact with the lower corner of the ruling-edge. The hand 
holding the pencil should be in a position similar to that of Fig. 10, 
page 27, steadied by sliding on part of the little finger. The pencil 
should always be drawn, not pushed. Thus, in general, lines are 
ruled from left to right and from the bottom up. 

15. The T-Square. The T-square is used with its head held firm- 
ly against the left-hand edge of the board. A line drawn with it in this 




FIG. 3 



position is called a horizontal line. Any number of horizontal lines 
may be drawn by sliding the T-square up or down. Horizontal lines 
are drawn from left to right, the pencil or pen being guided by the 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 4 



upper edge of the T-square blade. Do not use the lower (or nearer) 
edge of the blade. The T-square is held in position with the left 
hand pressing its head against the board, leaving the right hand free 
to draw the line. The T-square is not to be used with its head 
against the top, bottom, or right-hand edges of the board. If, how- 
ever, a draftsman draws with his left hand, he will need to use the 
T-square on the right-hand instead of the left-hand edge of the 
board. The habit should early be acquired of feeling the head in per- 
fect contact with the edge of the board before starting to draw a 
line. 

16. The Triangles. (a) The two triangles commonly used are 
shown in Fig. 3. One triangle has two angles of 45 each and a right 
angle ; the other has a 30 angle, a 60 angle, and a right angle. 
The first is called a 45 triangle, the second a 30 or 60 triangle. 
These triangles are used for ruling straight lines other than hori- 
zontal lines, for drawing parallel lines, for erecting a line perpendicu- 
lar to any other line at any given point, and for drawing lines at 
certain angles to the horizontal. Various other uses to which the 
triangles may be put will occur to the draftsman after he becomes 
accustomed to working with them. 



(b) Vertii'nl Lines. Vertical lines may be drawn with either tri- 
angle by placing a short side against the T-square. (See Fig. 3.) 

(c) Lines Making a Given Angle n'itli i1 //w/,:<//,/v/. A 15, 30, 
45 or n line is understood to mean a line making an angle of 15, 
30, 45 or n respectively with a horizontal line. By placing one 
edge of the 30 angle of the triangle against the T-square a 30 line 
can be drawn in four directions from any given point. By using the 
other angles, 45 and 60 lines can likewise be drawn. By combining 
the two triangles (Fig. 4 and Fig. 5) 15 and 75 lines can be drawn. 
Thus by means of the T-square and triangles a circle can be divided 




i. 



into twenty-four equal segments by drawing from its centre 15, 30, 
45, 60, and 75 lines in each of the quadrants formed by a horizon- 
tal and a vertical line intersecting at the centre of the circle. 

(d) To Draw One or More Lines Pamll,! f </ f ,'!/;>, Lhu\ Make 
any edge of one of the triangles coincide with the given line and 
bring an edge of a second triangle into perfect contact with one of 
the two remaining edges of the first triangle (Fig. (>*). Hold the 

* In Figs. 6, 7. 8, and 9 the original position of the first triangle is shown by the 
parallel line triiingle drawn on the paper. 



TIIK rsi-; OF THE DRAWING; IXSTUCMK.NTS 



25 



second triangle perfectly stationary and slide the first triangle upon 
it (Fig. (>). Either triangle may be used for the first one, a little prac- 
tice enabling one to choose the most convenient arrangement for any 

given case. 




FK;. (j 



(e) To l-'/'i i-t ,i I'< i'j>ini1i<'u/<(i- to any Lin< </f /i/,i/ (T!I;H Point. 
Make OIK- edge of the right angle of either triangle to coincide with 
the given line (Fig. T). Bring an edge of a second triangle into per- 
fect contact with the hypotenuse edge of the first triangle. Slide the 
first triangle upon the second, as indicated in Fig. 7. 

(f) Si-i'iiiul M' tlnxl. Make the hypotenuse edge of either triangle 
coincide with the given line (Fig. 8). Bring an edge (preferably the 
longest edge) of a second triangle into contact with one of the two 
remaining edges of the first triangle. Holding the second triangle 
stationary, turn the first triangle to the position shown in Fig. s. 
This method can often be used where the first method cannot. 

(ff) In all of the three methods here given, the greatest care should 
be exercised to prevent the stationary edge from slipping; the sec- 
ond triangle being held firmly in place with the left hand until the 



first triangle has been moved to the desired position ; the left hand can 
then hold both triangles, leaving the right hand free to use the pencil 
(Fig. !>). If only one line is to be drawn, it is evident that when the 
first triangle has been moved to its final position the second triangle 
need no longer be held in place. In large drawings it will often be 
found of advantage to use the T-square in place of the stationary tri- 
angle. 

17. The Ruling-pen. --To ink in a drawing well requires great 
care and some experience. The beginner should not attempt to ink 
in his drawing until he can make a clear-cut straight line with rea- 
sonable certainty. To insure this, practice inking straight pencil lines. 
It is good practice, also, to ink in squares, rectangles, and triangles 
until not only the lines themselves are good, but the corners and in- 
tersections also. Corners should be very definite. Be careful to stop 
each line at exactly the right point, for ragged corners and poor inter- 
sections indicate careless drafting. 

, Before starting to ink, try the pen on a piece of paper I //,>' tlmt 
a /Mm n-liii-h it ix t<i hi' nxed, to determine the proper width of line. 
(It is well to keep part of a sheet especially for this purpose.) Adjust 




FIG. 7 



26 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



the pen by means of the thumb- screw, opening or closing the nibs 
until a firm, clear line of medium width is obtained. If the line is 
ragged or the pen fails to work, it is probably because the nibs are 
not exactly of the same length, or because they are not sharp enough. 




A nib which is too short or too dull will leave its side of the line 
more or less broken. The ink oftentimes can be made to flow by 
moistening the end of a finger and touching it to the point of the 
pen. The best of pens become dull with use, and, as it becomes nec- 
essary, each draftsman should sharpen his own pen according to the 
directions of Art. 5. 

To fill the pen, insert a common writing-pen full of ink between the 
nibs. Prepared inks usually have some device for filling the pen in 
the stopper of the bottle, designed also to be inserted between the nibs. 
Another way is to dip the ruling-pen itself into the ink, wiping the 
outside of the pen clean before using. In whatever way the pen is 
filled no ink should be allowed to remain on the outside of the nibs. 
Do not overload the pen, but, on the other hand, before commencing 
a line be sure there is ink enough to last its length, as it is difficult 



to "piece" or continue a line after refilling the pen. The flow of ink 
will be much more satisfactory if the charge is kept from becoming 
so small as to cause the ink to dry or thicken in the point of the pen. 
In fact, the only way to draw fine lines successfully is by frequently 
cleaning and refilling the pen. 

The pen should be held almost perpendicularly, thumb -screw out, 
with both nibs pressing evenly on the paper (Fig. 10). The pen may 
be inclined d't<jld1ij in the direction in which it is moved, but the nat- 
ural and common error is to incline it too much. It is a mistake not 
to acquire early the correct method of holding the pen. The best pens 
incorrectly held produce poor lines. Do not press the side of the 




Fir, 9 



pen -point too heavily against the ruling- edge, as the nibs will be 
pushed together and the width of line will vary. A certain "touch," 
familiar to good draftsmen, brings the pen lightly but firmly in con- 
tact with paper and ruling-edge at the same time. Steady the hand 
by sliding on the end of the little finger. The pen should be moved 



THE USE OF TiiE DRAWING INSTRUMENTS 



L>7 




FIG. 10 



from left to right, and should be 
ili-'iirn. not jiiixlu'it. See that there 
are no small particles of dust or lint 
in its path. 

Never push the pen backward 
over a line. If a line is not well 
drawn the first time it is rather 
difficult to " patch it up." The best 
method is to go over it a second 
time in the same direction, tak- 
ing care not to widen the original 
line. Do not ink too close to the 
T-square or triangle, but place the 

ruling- edge so that it does not quite coincide with the pencil line. 
Endeavor to get into the easiest position to ink a line, even though 
it become necessary to walk around the drawing. (For this reason 
manv draftsmen prefer to stand while inking.) Keep the ruling- 
edge between the line and the body, so that in moving the pen the 
tendency is to draw it against the ruling-edge, otherwise the pen is 
apt to be pulled away from it, making a break in the line. When 
the line is inked remove the T-square or triangle by drawing it away 
from the line or towards the body to avoid blotting or blurring. 

When several lines meet in a point, if possible ink. from and not 
tmi^irih the point, otherwise too much ink will gather at the intersec- 
tion of the lines. Allow one line to dry before inking another. The 
same precautions are necessary in inking acute angles. 

If the top or left -hand lines are inked first, and the draftsman 
works rfnwn or to the right respectively, time will be saved which 
would otherwise be lost in waiting for lines to dry. In inking in 
small details, place one triangle so that the lines to be inked lie with- 
in the open space in the centre of the triangle. A second triangle can 
then be laid across the first and used as a ruler in any direction with- 
out blurring wet lines. 

When the pen is set at the proper width, avoid changing its nibs 
until all lines of that width are inked. The pen is easily cleaned by 



placing a piece of cloth between the blades and forcing it out through 
the end without loosening the thumb-screw. India-ink dries quickly, 
therefore do not lay the pen aside for any length of time without 
cleaning. Ink left to dry in the pen will almost surely corrode the 
points; for this reason the pen should be kept bright and clean when 
not in use. 

18. The Compasses. (a) Before using the compasses adjust 
them as follows : Insert the pen attachment in place of the one contain- 
ing the pencil lead. Set the needle-point so that the pen-point and the 
shoulder on th,e needle-point are even when the compasses are closed. 
Eeplace the pen by the pencil lead (previously well sharpened), and 
adjust the latter so that it is even with the needle-point when the 
compasses are closed. The needle-point can now be used with either 
pen or pencil without being reset, the 
pencil alone needing readjustment 
from time to time as it wears off. 
Of the two ends of the needle, the 
one with a shoulder should be used, 
as it is designed to keep the point 
from making alarge hole in the paper. 

(I) In using the compasses bend 
both legs so that each will be perpen- 
dicular to the paper when the arc 
or circle is drawn (see Fig. 11). Be 
particularly careful to do this when 
the pen attachment is used, for in 
no other way can the nibs of the penbe made to bear evenly on the 
paper. 

(c) Most compasses are provided with a cylindrical handle at the 
head. In using the compasses, hold this handle rather loosely between 
the thumb and forefinger, and let it roll between the two during rota- 
tion. Allow the compasses to lean a little in the direction of revolu- 
tion (which is clockwise), and bear down slightly on the pen or pencil, 
but not on the needle-point. In inking, however, the latter should be 
firmly fixed in its proper place before touching the pen to the paper, 




FIG. 11 



28 



AN INTRODUCTORY COURSE IN MECHANICAL DRAW] Mi 



otherwise it is apt to slip. On the other hand, the hole made by the 
needle-point should be as small as possible. When a point is used as 
a centre for several arcs or circles, extra care is necessary to pre- 
vent the hole from becoming too large, in which case it will be un- 
sightly, and will prevent accurate work. In setting the needle-point 
on any particular centre, guide it to place with a finger of the left 
hand. 

(d) The circumference of a circle should be inked with one contin- 
uous motion, an even pressure of the pen upon the paper being kept 
throughout. Stop the pen exactly at the end of one revolution, lest 
the line be made uneven by further inking. 

(e) Circles and arcs of circles should be the first part of a drawing 
to be inked in, as straight lines are more easily drawn tangent to 
curves than the reverse. 

(f) The lengthening bar is used for arcs or circles of greater radius 
than can be drawn with ordinary compasses. For very large arcs. 
" beam compasses," designed for the purpose, are used. For circles of 
one inch diameter or less, " bow compasses" are used, ordinary com- 
passes being too clumsy for such small circles. 

(g) Note that many of the directions for the use and care of the 
ruling-pen, such as filling, cleaning, sharpening, etc., apply also to the 
pen belonging to the compasses. 

19. The Dividers. Dividers are chiefly used for dividing a line 
into any number of equal parts, and for transferring distances from 
one part of the drawing to another. Tlteij xlmuld not be used for 
transferring distances from scale to paper. Compasses can be used as 
dividers, but the accuracy attained will not be as great. 

Let it be required, for example, to divide a line into seven equal 
parts. Open the dividers until the space between the two points is 
equal, at a guess, to about one-seventh of the length of the line. Be- 
ginning at one end, step off seven spaces on the line. Suppose the 
last point falls short of the end of the line by about one-half an inch. 
Since the error has been multiplied seven times, make the space be- 
tween the points of the dividers about one-fourteenth of an inch 
greater than before, and apply the dividers seven times again. Thus, 



by trial, the error is constantly reduced until the dividers are set cor- 
rectly. (Three such trials at the most should be sufficient.) In using 
the dividers in this way. one or the other of the points is always on 
the line, the two points alternating front and rear. The point in front 
is used as a pivot, the semi-revolutions being alternately to the right 
and left of the line. In doing this, it is not necessary to make holes 
in the paper. Accuracy and neatness require that the points of the 
dividers should simply rest on the surface of the paper. 

When a distance to be transferred from one part of the drawing 
to another cannot easily be laid off with the scale, the dividers are 
used. The thumb-screw is for opening or closing the dividers slowly, 
and its value is evident in setting the points to a known distance. 

20. The Scale. (W) Much time maybe wasted by the faulty use 
of the scale. To lay off distances, place the scale on the paper and 
mark points with the round-pointed lead of the pencil, making sure 
they come exactly opposite the proper divisions on the scale. In 
measuring distances along a line, the edge of the scale should, of course, 
be close to the line throughout its length. Do not transfer distances 
from scale to paper by means of the compasses or dividers. Never 
use the scale as a ruler. 

(J) It is evident that there are many objects, the drawings of 
which cannot be made full size and come within the limits of the 
paper; they are accordingly drawn to a reduced "scale." When, on 
the other hand, objects are very small, it is often convenient to make 
the drawing to an enlarged scale. The ordinary method of making 
such drawings is to assign to the inch an arbitrary value, so chosen as 
to make the drawing the desired size. Thus every inch on the scale 
may represent a foot on the object, in which case the scale is said to 
be "one inch to the foot." If one inch represents four inches, the 
scale is " three inches to the foot," or quarter size, and so on indef- 
initely. Sometimes the scale is very small, as in map-work, where 
one inch often represents several hundred feet. When one inch rep- 
resents two inches the scale is simply " half size." 

There are special scales made for this kind of work, the use of 
which is explained in Art. 21. If an ordinary scale is used it is better 



TIIK USE OF THI-: HI;A\VIX<; INSTKI'MKNTS 



2!) 



(unless the drawing is made " half size") not to reduce the dimensions 
of the object by arithmetic, but to read directly from the scl< ifx<tf. 
This becomes easy by c/ii/in/iiii/ in flu 1 mi ml tin- value of each i/irixi<i 
(/*, scale. Thus, if making the drawing "one inch to the foot," 
think of each inch as representing one foot. To lay off six feet three 
inches one would at once go to the six-inch mark and then to the 
quarter-inch mark beyond. Again : If the scale is three inches to the 
foot, or '-one-fourth size," think of each inch as representing four 
inches and each quarter inch as one inch. To lay off six and one-half 
inches one would count off six quarter inches (or, better still, go at 
once to the one and one-half inch mark), and one-eighth of an inch 
bi-vond would be the required point. It is frequently necessary to 
estimate small distances. If, for example, in the first illustration it 
had been required to lay off six feet two inches, one would go two- 
thiril* of the quarter inch beyond the six-inch mark, it is in such 
cases that the special scales are of distinct advantage. (See Art. 21.) 
81. Architect's Scale! The end space of the architect's scale is 
divided into twelve equal parts. For example, on the scale used for 





-o 




% 


Mill . i ' 






OI2C 

1 


5 

> 


1 


1 1 1 1 i i 1 ! 1 






/ n 






FIG. \'l 





1 in. = l ft., the end inch is divided into twelve parts, each one of 
which i'1-jn'wiilx an inch. The other inches are not thus subdivided, 
but are numbered, the zero point being between the first and second 



inch. Thus the second inch from the end of the scale is marked 1, 
the third 2, and so on. To lay off 2' 10", for example, from a point, 
place the mark 2 at the given point ; zero on the scale will then be 
two feet away, and (since the end space is divided into twelfths) ten 
spaces beyond zero will be opposite the point required. (See Fig. \-2.) 

The other scales referred to in Art. 8 are constructed and used in 
a similar manner. Inspection of Fig. 12 will make clear, for example, 
how 3' -i" would be laid off with a scale of f in. = l ft. 

End spaces are often divided into twenty-four or forty-eight equal 
parts, in order that half-inches and quarter-inches can be read off. 

22. The Curve-ruler. (a) To ink in a curve smoothly by means 
of a curve-ruler is one of the most difficult things a draftsman has 
to do, and nothing but persistent, careful practice will enable one to 
attain satisfactory results. A series of points through which the curve 
must pass is given. Sketch the outline in pencil, free-hand, through 
these points, and ink in small portions with the curve-ruler, drawing 
from left to right. The curve will coincide with the pencil outline 
for a short length only, and great care is necessary to make the differ- 
ent sections join well. To insure a smooth curve, it is well to let the 
edge of the ruler coincide with a small portion of the curve beyond 
the points where any particular section is begun or stopped. In ink- 
ing, always keep the blades of the ruling-pen tangent to the curve by 
allowing the handle to turn between the thumb and fingers. 

(b) In inking parabolas, hyperbolas, and similar curves with a 
sharp turn, the common difficulty is in avoiding a slight angular 
break in the curve at the turn. The part of the ruler used for one 
side of the bend should be such that if the line were continued it 
would nearly coincide with the curve for a short distance the other 
side of the bend. When the ruler is reversed for the curve on the 
other half of the turn, the angular break referred to should not result. 
A small portion of a narrow turn can usually be better "drawn with 
the bow compasses than with the curve-ruler. 



CHAPTER III 
WORKING KNOWLEDGE* 



23. To Fasten the Paper to the Board. (a) Fasten the paper 
(one sheet only) to the board by means of thumb-tacks, one in each 
corner, pressed down until the heads are flush with the paper. Insert 
a tack in one corner, make the paper square with the board by means 
of the T-square, stretch it diagonally across to the other corner, and 
insert a second tack; stretch the paper diagonally in the other direc- 
tion and insert tacks. It is not so essential to have the paper square 
with the board as to have it stretched flat and smooth. In large sheets 
it may be necessary to put additional tacks along the edges. A tack 
can be temporarih 1 - removed when it interferes with the work. 

(b) In certain kinds of work the best results can only be obtained 
by stretching the paper while damp. This is done by moistening the 
whole sheet, with the exception of a border of half an inch on the 
outside, until it is limp. Secure this dr}' border to the board with 
mucilage, which must set before the body of the paper dries, so that 
the latter may be stretched uniformly by its own contraction. Use a 
sponge in smoothing the paper and work from the centre out. In 
gluing the edges commence with the centres of opposite edges, leav- 
ing the corners until last. Cut the paper from the board when 

* Skill in handling the instruments must be supplemented by a general knowledge 
of the methods of work. The nucleus of this "working knowledge" can be early ac- 
quired from a few important directions based on common experience. There are many 
habits of accuracy and little devices for time-saving which are second nature to a good 
draftsman, and which go so far towards making one an expert. Once started right, the 
draftsman's own experience is his best teacher. 

The foot-note at the beginning of Chapter II. applies to this chapter also. 

Arts. 23 to 33 are to be read before the first plate is drawn. Arts. 34 to 45 are put 
in this chapter for convenience of reference later in the course. 



the drawing is finished, following the edges around successively in 
order. , 

(c) Dealers in paper endeavor to keep it flat ; the draftsman should 
keep it flat also. If kept in rolls it will not lie smoothly on the board 
unless it is first wet and stretched according to the above method. 

24. Precautions to Insure Neatness. The paper and instru- 
ments must be clean to start with, and kept so, if possible. The tri- 
angles and T-square are liable to become dusty. It is well to wipe 
them with a damp not a wet cloth before commencing work, and as 
often afterwards as necessary. The paper should be kept clean by 
means of a stiff brush or a silk or linen handkerchief. There is little 
danger of applying the brush or handkerchief too frequently. After 
the eraser has been used, always brush the surface of the paper clean 
before proceeding with the work. 

In inking, watch the paper in front of the pen, and if a particle of 
dust or lint gets in the path, blow it away before it can get into the 
pen and spoil the line. Beware of wet lines or a pen too full of ink, 
or dropping the pen on the paper most common causes of blots. 

25. Arrangement. (a) The pleasing appearance of a sheet of 
drawings depends largely upon the arrangement of the different parts 
or figures. The appearance as a whole should be symmetrical ; this 
is secured by the judicious spacing of the figures with respect to each 
other as well as to the edges of the paper. It is often difficult to esti- 
mate the space which any one figure will occupy when drawn, or 
what the general effect will be when compared with the other ad- 
jacent figures. No general rule can, be given, but the attention of the 
draftsman is called to this point as one of importance. 



WORKING KNOWLEDGE 



81 



(b) A border line more or less elaborate can be used with good 
effect where the drawing itself is more or less elaborate. A single 
heavy line, or a heavy line with a light line just inside of it, will 
usually make the most suitable border. One needs to be quite 
sure that his drawing is elaborate before adding a fancy border. 
When there are several sheets of drawings of the same object, it is 
customary to make the different sheets and borders of one size. In 
simple, plain drawing, it is, perhaps, in better taste not to put any 
border on at all. 

(c) It is well to note here that while the figures of the plates of this course are per- 
haps too simple to require border lines, nevertheless for convenience in locating the 
problems such lines are drawn. In each plate, unless otherwise noted, the space wilhin 
the border lines is divided into as many equal rectangles as there are problems, and 
each figure is located symmetrically with respect to the sides of its own rectangle. It 
is evident that such a method of arrangement would avail little had not each figure 
been previously designed to fit into its assigned place. In some cases it has been 
thought desirable to locate the figure exactly, the distances of some starting-point from 
two sides of the rectangle being given at the end of the printed problem. (See page 2.) 

26. Rapid Drafting. () A rapid draftsman is not only quick 
with his instruments, but he also uses the best methods and does 
things in the most economical order. He builds up a figure intelli- 
gent!}', looking ahead as far as possible. The skeleton outline, or 
"limiting lines," are drawn first, the details last. Like operations are 
grouped. All lines which can be drawn with one position of the 
T-square or triangles are finished before commencing another set of 
lines. When the scale is in hand, all necessary measurements which 
can be made at that time are laid off. 

(J) All arcs or circles which can be described with a single setting 
of the compasses are drawn before changing that setting. Unneces- 
sary pencil lines are left out the fewer construction lines, as a rule, 
the better. One can save time by knowing what to slight and what 
not to slight. The same care is not necessary for all classes of work 
nor for all operations on the same drawing. This is especially true 
of the preliminary work in pencil, as is more fully stated in Art. 27. 
Many similar hints for rapid drafting could be given, but the above 
should suffice to start the beginner on the right track. 

(c) It may be hardly necessary to add that steady rather than hasty 



work is to be desired. Undue haste on the part of the beginner usu- 
ally means failure more or less complete. The most skilful draftsmen 
are obliged to be careful how they hurry. 

27. Pencilling. (a) Drawings are usually made in pencil and 
then inked in. In working drawings, instead of inking the pencil 
lines a tracing of them is usually made. (See Arts. 43 and 148.) 
Pencil clearly but lightly. A III1HH pencil may be used if the 
drawing is to be traced without previous inking, otherwise use a 
IIHIIHIIII pencil. 

(b) Care should be taken to draw accurately in pencil. The pencil 
lines should be true guides for the inking-pen. It is the common ex- 
perience that the accuracy of a drawing is seldom improved upon in 
the inking in. Thus, for example, when parallel lines should be \" 
apart, as in Prob. 1, Plate I., if they are not exactly \" apart in pencil 
they are not apt to become so when inked in. On the other hand, it 
is not necessary to stop each pencil line at exactly the right place. 
The same care is necessary in making the ink lines stop Avhere they 
should, whether the pencil lines do or not. It saves time, therefore, 
and in some cases makes the intersections and corners more definite 
to let the pencil lines overrun slightly, the projecting ends being 
erased after the whole drawing has been inked in. Likewise in draw- 
ing a pencil line along which a given distance is to be laid off, make 
it a little longer than necessary and then mark off the required dis- 
tance, leaving the ends to be erased later. 

It is often unnecessary to draw a line from end to end, especially 
if it is a construction line. For example, in drawing two diagonals to 
find the centre of a rectangle, draw an inch or less of one line near the 
centre, and simply cross it with the other. Many similar cases occur 
in all construction work, where time would be wasted and unneces- 
sary erasing caused by drawing entire lines. 

28. Inking. (a) As a rule, do not commence to ink a drawing 
until it is finished in pencil. The width of line to be used varies with 
the size of the drawing the larger and more open the drawing the 
coarser the lines may be. Lines should not, however, be so coarse as 
to make the drawing seem crude, nor so fine as to make it indistinct. 



32 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



Lines of medium width are best suited for open plain figures, like 
those in the plates of this course. It is always well to test a pen after 
setting its nibs to see if the line is right, but this should not be done 
on the sheet itself nor on the drawing-board. A separate piece of paper 
should be kept at hand for this purpose. 

(I) It is sometimes necessary to ink in a line of unusual width, 
as, for example, a heavy border. The safest way of doing this is to 
draw several parallel lines of medium width, about their own thick- 
ness apart, and fill in between with another set of parallel lines when 
the first are dry. Another and more common method of inking 
such a line is to draw the two outside edges and fill in between 
with a brush or with heavy lines from the inking- pen. In very 
wide lines this too often results in leaving a large quantity of ink, 
which warps the paper and takes a long time to dry. 

29. Erasing. (a) It is well to avoid erasing pencil lines until 
the drawing is nearly finished. Many draftsmen prefer to leave the 
erasing until after the drawing is inked. If the eraser must be 
used, as, for example, to correct the pencil drawing, the surface of the 
paper should be brushed clean again before anything else is done. If 
the eraser does not of itself wear off fast enough to keep clean, rub it 
occasionally upon the drawing-board, allowing some particular spot on 
the wood to be worn clean and remain so for this purpose. In erasing 
after the drawing has been inked, avoid rubbing across ink lines, but 
erase in between, otherwise the lines are apt to become dimmed or 
blurred if not thoroughly dry. Much erasing with the pencil-rubber 
will deaden any ink line, destroying the sharp, black effect. 

(b) To make corrections on inked drawings, use a hard rubber ink- 
eraser. Do not press too heavily on the paper, as no time is saved in 
this way, and it injures the surface for further inking. For the same 
reason lines should seldom be scratched out with a knife. An excep- 
tion occurs when a "dashed" line has been inked in full by mistake. 
A full line is easily made "dashed" by taking out short portions of it 
at regular intervals with a crosswise motion of the knife-point and 
smoothing over the breaks with a pencil-eraser. The surface of large 
blots may be removed with a knife before the eraser is applied. If 



the surface of the paper is injured in erasing, rub briskly with a clean 
hard substance (ivory is good) until the paper becomes "polished" 
and ready for the ink. 

(c) When it is desired to erase a portion of a drawing and leave 
adjacent portions untouched, cover the part not to be erased with a 
triangle. The erasing can then be carried clear to the latter's edge, 
but no further. Thus, by shifting the triangle, as much or a,s little of 
the drawing as desired can be erased. A flat piece of celluloid, with 
a straight narrow slit in it, is useful in erasing portions of lines, the 
rubber being applied through the slit. A sponge rubber or crumbs of 
wheat-bread can be used to clean the drawing when finished. 

30. Laying off Measurements. () In laying off several suc- 
cessive distances on a line, set the scale once for all and then do not 
move it. For example, suppose it is required to lay off five successive 
spaces, \", $", |", 1", and 1 J" long respectively. Place the edge of 
the scale along the line with its zero point at the starting-point. The 
spaces would then be marked off opposite the |", f ", 1", 2", and 3|" 
divisions of the scale. In this way the last division (3f ") equals the 
sum of all the spaces. A wrong method is that in which the zero 
point of the scale is moved up each time to the end of a space to lay 
off the next space. Thus an error in a single space affects all succeed- 
ing spaces as well, and an opportunity for errors to accumulate is 
thereby afforded. This is not true of the first method. 

(?>) In very accurate work, a needle set in a wooden handle is use- 
ful for marking distances. Very small prick-marks are made, which 
are easily kept track of if small, free-hand pencil cirples are drawn 
around them. 

(c) Many times measurements, having once been laid off, can be 
projected on to other lines by means of the T-square or triangles. It 
may be also noted that the eye can become so trained that small dis- 
tances can be estimated with surprising accuracy. Thus, in certain 
classes of work, much tedious use of the scale is avoided. 

(d) In order that the diameter of a circle may be exactly right, 
mark off its radius on a straight line each side of a point, anil open 
the compasses until the circumference of the circle passes through the 



WORKING KNOWLK] HJK 



33 



extreme points. This is better than to take the radius directly from 
the scale, although the latter method is sufficiently accurate for ordi- 
nar\ T work. 

(< i Do not lay off distances with the compasses or dividers when 
the scale can be used. 

(f) Time and annoyance will be saved in the end if the drafts- 
man will form the habit of frequently checking his measurements. 
Simple inspection with the eye alone will usually detect large errors, 
and it is wise to look occasionally at the drawing as a whole. For 
small errors, apply the scale a second time wherever there is the least 
doubt of accuracy. Many other ways of applying checks will occur 
to one as the work progresses. 

31. Use of the Triangles. The beginner is warned against 
trusting to the extreme corners of the triangles, as they soon become 
rounded. A common error is the attempt to use one triangle alone. 
For example, if a 30, 45, 60, or perpendicular line is to be drawn to 
a horizontal line, it is wrong to make one edge of the triangle coincide 
with the given line and then draw the required line by means of an- 
other edge. In this case the T-square should be in a horizontal posi- 
tion a little below the given line, and the triangle is held against it. 
Thus a triangle is almost always used against the T-square or another 
triangle, except in inking. 

32. Line Notation. Custom differs in respect to line notation. 
In addition to the ordinary full lines, the following ink lines will be 
used in this course : 

(a) Invisible lines of an object, such as rear edges, are represented 
by dashes from -fa" to -J-" long ; the spaces between should be as short 
tin juixx'ihle and still have the dashes distinct from each other. The 
thickness of line is the same as for ordinary full lines. 

(b) Construction lines and projecting lines are lighter and more 
delicate than "invisible lines," consisting of little dashes as short and 
fine as can well be made. The object sought is to make the drawing 
itself stand out boldly, while the construction lines seem in. the back- 
ground. 

(c) The axis of a figure should be inked in with a short and a long 

3 



dash alternating; the long dash should be a little more than -J-" long, 
the short dash a little less than -fa" long. 

(d) T/te trace of a plane is represented by a dash and a dot alter- 
nating ; the dash should be about " long. When the trace is invisible 
there are two dots between the dashes. 

Care should be taken in drawing the above lines to secure an even 
appearance by making the spaces very short and the dashes of uniform 
length. Nothing tends to give a more finished appearance to a draw- 
ing than well-drawn " invisible " and " construction " lines. When 
too hastily drawn they can seriously mar an otherwise excellent 
drawing. 

33. Lettering the Drawing. Letters and printed words on a 
drawing should in general be either horizontal or vertical, being read 
from left to right and from the bottom up respectively. They should 
be printed in the open spaces in such a way as not to obscure the 
drawing. 

Free-hand lettering is done with an ordinary writing-pen. For 
heavy letters a ball -pointed pen is used. Every draftsman should 
learn to letter well. The appearance of a good drawing can be spoiled 
by poor lettering. Good lettering consists of plain, even, clear-cut 
letters, well proportioned, well spaced, and quickly made. 

The beginner will do well to draw pencil guide-lines for letters 
and words. If the letters are made small and close together, it will be 
easier to space them properly. Most letters are not printed with a 
continuous stroke, as in writing. In forming each letter much de- 
pends on the number of strokes, the order or sequence of strokes, and 
the direction in which the pen is moved, instructions for which are 
admirably given in " Lettering for Draftsmen, Engineers, and Stu- 
dents : a Practical System of Free-hand Lettering for Working 
Drawings," by Charles W. Eeinhardt. If the student will get this 
book and carefully follow its directions, he can hardly help acquiring, 
with a reasonable amount of practice, a neat, legible style of free- 
hand lettering. 

The greatest precision in lettering (especially if the letters are 
large) is only attained by the use of the drawing instruments, and 



34 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



when the results warrant the extra time expended, draftsmen resort 
to this method. Letters made in this way should be well propor- 
tioned and well spaced. A text-book on " Plain Lettering," by Prof. 
H. S. Jacoby, is a very complete treatise on the accurate proportion- 
ing and spacing of letters. The Roman, Gothic, and other standard 
letters required by draftsmen are treated in detail, and numerous 
examples of titles and printed notes given. 

34. The Use of Colored Inks. The use of colored inks is only 
desirable when it makes the drawing more easily understood. Aside 
from black, red is the color most commonly used. Construction lines 
and "dimension lines" (see Art. 149) are sometimes inked in red. 
Non-essential or subsidiary parts of a drawing, introduced for the 
purpose of making the main drawing clearer, can be kept in the back- 
ground by using red ink, especially when a tracing (see Arts. 43 and 
148) is made. Thus, when two parts of an object fit together, and 
one part has already been made or provided for; in a drawing of the 
second part, the first, which ordinarily would not appear at all, is 
sometimes drawn in red ink to better show the connection. In 
maps and profiles, proposed lay-outs and grades are usually drawn in 
red to distinguish the new from the old. 

35. To Mix India-ink. For fine work it is safer for the drafts- 
man to prepare his own ink from Chinese stick-ink. This is done as 
follows : Place as much water in the saucer as will suffice for the 
amount of ink required. Rub the end of the stick on the bottom of 
the saucer with a rotary motion until the mixture is of the desired 
density. The liquid will appear black before it really is ; to get it 
just right, test it in the inking-pen. It should flow readily, dry quick- 
ly, and the resulting line should be jet black, and not easily erased or 
blurred when dry. If the line fades as it dries, add more ink to the 
mixture from the stick. If it lacks the other desired properties, try 
another make of ink. Chinese inks vary in quality, but it does not 
follow that the most expensive kinds are the best. Try different 
sticks until one is found which i's satisfactory. Wipe this dry after 
using to prevent it from crumbling, and it will last for a long time. 
The following precautions should be observed : Clean the saucer be- 



fore using. Avoid dust or undissolved particles of ink in the mixture 
they clog the pen. Keep the mixture covered when not in use. Do 
not use ink more than two or three days old, but mix a fresh supplv. 
Do not try to use ink which has dried in the saucer. 

Colored inks may be prepared from artists' water-color cakes in a 
similar manner. 

36. Shade Lines. (a) Edges of an object which lie between 
light and dark surfaces are often represented by lines about twice as 
wide as other lines. Such lines are called shade lines. They are fre- 
quently omitted, especially in working drawings. They add, however, 
to the appearance of a drawing, and when properly constructed are of 
value in understanding or reading it. Directions for their use (which 
differs in different kinds of drawing) will be found in Arts. 53, 128. 

(5) In shading a circle only part of the circumference is made 
heavy, the line gradually decreasing each way until it merges into the 
original width. To produce this effect, first draw the circle with the 
ordinary width ink line. Imagine a line drawn through the centre of 
the circle to that point of the circumference where the greatest width 
of line is desired. Shift the needle-point a very little from the centre 
along this line either towards or away from the point on the circum- 
ference, according as it is desired to have the extra thickness fall out- 
side or inside the original line. An arc can now be drawn which will 
start from the original circumference, deviate farthest from it at the 
desired point, and come back to it again in such a way that it cannot 
be seen where it begins or stops. It requires some care to prevent the 
needle-point from slipping back into the original centre. The setting 
of the compasses should not be changed from that used in drawing 
the original circle. 

(c) A second method (which is not recommended to beginners 
unless used with great care) is to keep the same centre and .*/>,-/ /i>/ 
the compasses by pressure of the hand, making the point of the pen 
gradually deviate from the circle and return again, thus giving the 
increased thickness of line on part of the circle. This is a quick meth- 
od and satisfactory in the hands of an experienced person. 

37. Line Shading. Parts of a drawing representing curved 



WORKING KNOW LEI >G E 



surfaces are sometimes shaded by means of parallel lines of different 
widths and distances apart, so drawn as to produce a variation of 
shade corresponding as nearly as possible to that on material objects. 
This effect is obtained by gradually increasing the width of lines, at 
the same time diminishing the distance apart, or vice versa. This 
kind of shading does not have the soft and finished appearance ob- 
tained by some of the other methods, but it is useful in many cases. 
In practising bv oneself much help may be derived from the many 
excellent advertising cuts which appear in the engineering papers and 
periodicals. 

Line shading can be executed with comparative ease on cylindrical 
surfaces, but is very difficult on cones and spheres. It will be found a 
thorough test of the ruling-pen, because it requires all widths of lines 
down to the very finest, and any ragged or irregular edges will be 
brought into surprising prominence. For examples of line shading, 
Bee Plate III., page 105. 

38. Parallel-line Shadows. Shadows on different parts of an 
object are sometimes represented by parallel lines similar to section 
lines the darker the shadow 7 , the closer together the lines. By a 
judicious use of such lines, especially in isometric, cabinet, and per- 
spective drawings, the object may be made to "stand out," and the 
effect will be more satisfactory than that produced by a simple outline 
drawing. 

39. Section Lines. When an object is cut in two by an imag- 
inary plane (see Art. 90), that part of the drawing representing the 
portion of the object cut is cross-lined with parallel lines called section 
IliH'tt. These lines are usually 45 lines in one direction or the other, 
drawn about ^" to " apart. The larger the section the farther apart 
the lines, and the farther apart the lines the easier it is to secure a 
uniform appearance. The distances apart are made equal by the eye 
alone, not by actual measurement. The tendency on the part of a 
beginner is to make the lines too near together and the spaces un- 
equal. The lines are not to be first drawn in pencil ; even if the draw- 
ing is to be traced, better results will be secured by drawing the 
section lines once only, and then in ink. When two different pieces 



meet, the section lines in one should slope in the opposite direction 
from those in the other. Section lines should be much finer than the 
ordinary lines, hence ink slightly thinned best serves the purpose. It 
is better to leave small open spaces for letters and figures than to 
render them obscure by drawing section lines over them. 

Many "section liners" designed for drawing parallel lines are to 
be had. Some of these are very useful, but a draftsman should be 
able to section-line nicely without them. Drawing section lines for 
any length of time is trying to the eyes. In such a case, or where 
considerable accuracy is required, it is better to use a section -liner. 
The "Sphinx," an inexpensive section-liner made by Weber & Co., 
Philadelphia, is recommended. 

As in the case of line shading, excellent examples of section lining 
are to be found in cuts of machinery in engineering papers. 

40. Tinting. (a) Tints are chiefly used in map-work, where flat 
tints of different colors* are laid on to distinguish the different por- 
tions of the map. Colors are also employed in working drawings to 
represent different materials. When it is desired to represent a shadow 
cast by an object, or to shade the drawing of the object itself, gray 
tints made of India-ink are used. 

(I) For colored tints, cakes of water-colors prepared for the use of 
artists are best. To mix either the colored or the gray tints, proceed 
in exactly the way described in Art. 35, but make the mixture much 
less dense, rubbing the stick on the end of the finger frequently dipped 
in water, instead of on the bottom of the saucer. Tints for shadows 
should be light' gray, not black. WHien a ven r dark tint is required, 
it is better to put on several successive layers of a lighter shade, wait- 
ing each time for the preceding one to dry, than to attempt a single 
dark tint at first. 

(c) The surface to be tinted must be clean. All pencil lines within 
the boundary should be avoided ; if drawn and not erased, they can 
be seen through the tint; if they are erased, the surface of the paper 
is injured and a smooth, even wash cannot be laid on. It is well to 
tint before inking. If the drawing is inked first, water-proof ink must 
be used. In shadow-drawing, do not ink in the outline of the shadow. 



36 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



(d) The rear of the board should be elevated a little so that the 
surface may be sloping. If the top of the drawing-table cannot be 
inclined, block up the board. The brush used is described in Art. 2. 
Take the tint from the surface with the side of the brush to avoid 
specks of ink in the bottom of the saucer. Small particles of ink 
transferred to the paper will dissolve and leave small blots. Apply 
the brush moderately full of the tint to the upper left-hand corner 
of the outline and draw towards the right. This will leave a small 
" pool " of tint, which must be worked down the paper, moving the 
brush across from side to side. This pool should almost, but not quite, 
run down the paper of itself. It must be kept full by additions from 
time to time with the brush. The tint must not be painted on. The 
secret of success is to coax the tint down the paper, keeping it moving 
all the time, and not allowing it to stand in one place longer than in 
another. In laying on the same wash, do not go over a place twice 
to " touch it up "; it will usually make it worse. The whole opera- 
tion must be done rapidly ; it is better to let the brush overrun a little 
OUTSIDE the outline than to spend too much time on the edges, allow- 
ing the interior of the tinted space to dry and become streaked. The 
tint outside the boundary line can be removed when thoroughly dry 
by covering the portion not to be erased with a triangle (or curved 
ruler, if the outline is curved), and using a pencil-eraser. 

(e) When the " pool " reaches the bottom of the outline, squeeze 
the brush comparatively dry- it will then take up the surplus tint 
like a sponge. The whole surface should now have a uniform flat 
tint. Better results are usually obtained if the surface is previously 
gone over with clean water, precisely as in tinting. When the sur- 
face, held towards the light, ceases to glisten, the tint can be laid on a 
little more leisurely and carefully, because it is not so quickly absorbed 
by the paper, and therefore dries more slowly. If the paper is too 
wet, the tint will run. 

41. Graduated Tints. Curved surfaces are not shaded uniform- 
ly, as described in the last article, but successive layers of tint are ap- 
plied, each covering a wider area than the preceding. Thus, to shade 
a cylinder, lay a narrow strip of tint along the element of darkest 



shade. When dry, apply a second strip a little wider than the first, 
and so on. If these successive layers overlap each other uniformly, a 







TJT 






FIG. 13 

fairly good effect is produced. But this method will always show 
streaks where the different coatings overlap. To make a perfectly 
continuous gradation, it is necessary to soften or draw out the edge of 
each strip while it is still wet, using clean water in the brush. A 
double-ended brush will be found convenient for this process, one end 
for tint and the other for water. This work must be done quickly, 
for the edges cannot be softened after they have begun to dry. 

Brush-shading requires great care and dexterity, and considerable 
practice is necessary to do it well. 

42. Blue-print Process. It is evident that in many cases more 
than one copy of a drawing is required, especially if it is a working 
drawing. The blue -print copying process, used almost exclusively, 
may be briefly described as follows : The original drawing is traced 
on transparent cloth or paper prepared for that purpose. Paper sen- 
sitive to light is also required. This paper is prepared by covering 
one side of a clean white sheet of ordinary tough, smooth paper with 



\\OKK I. \<i KXOWLKI ><;]; 



a chemical wash, and drying it in a dark room. If the prepared paper 
is washed before being exposed to the light, the water will remove 
the chemicals, and the paper will be as white as it originally was ; but 
if exposed and then washed it will become a permanent blue. If the 
tracing is laid over the paper when exposed, the light cannot pen- 
etrate the ink, and that part of the paper directly beneath the lines 
will remain unturned. If the prepared paper is then washed, a white 
drawing on a blue background will result. It is evident that any de- 
sired number of prints can be made from the same tracing. 

The prints are usually taken in a printing-frame, which has some 
device for holding the tracing and the sensitive paper flat and smooth 
against a glass front. The side of the tracing-cloth or tracing-paper 
upon which the drawing has been made is placed next to the glass, 
and the chemically prepared side of the process paper is next to the 
tracing. 

43. Tracings. Tracing-cloth of different widths can be had by 
the yard or roll. One side of the cloth is smooth and glazed, the 
other rough and dull. The drawing can be made on either side. Ink 
lines can be best erased from the glazed side a point in its favor. 
Blue-prints will also be slightly clearer if the smooth side is used. 
Sometimes the drawing is made directly on the tracing -cloth, and 
then the dull side is preferable, because pencil lines are more easily 
drawn on it. 

After completing a drawing in pencil in the usual way, pin the 
tracing-linen .over it the lines underneath will be plainly visible if 
they are moderately heavy and ink on the transparent cloth. The 
latter should be stretched flat and smooth. Before beginning to 
ink, sprinkle the surface with powdered chalk and rub gently with a 
soft cloth. This is necessary to make the tracing-cloth take the ink, 
especially when working on the glazed side. Specially prepared chalk 
in a box with perforated cover is the most convenient form for use. 
A sharp inking-pen is required for tracing it is more important 
than ever that the pen should be just right. 

Tracing-cloth is very susceptible to moisture, and if left on the 
board several days is liable to become ruffled and uneven by its ex- 



pansion. All important lines should therefore be traced the same 
day, if possible. As a further precaution, tear off a strip about half 
an inch wide from each of the two edges of the cloth before pinning 
it down. 

Ink dries more slowly on tracing-cloth than on ordinary paper, 
and care must be taken to avoid blotting the moist lines. If the 
cloth is of poor quality, the ink is liable to strike through and spread ; 
such cloth is useless for tracing. Eed ink does not print well, but is 
used to some extent for dimension lines or other portions of a draw- 
ing which it is desirable to render less prominent. 

Lines, letters, and figures should be made heavier on tracing-cloth 
than on an ordinary drawing, in order that the blue -print may be 
clear. It is not unusual to find a beginner carefully putting on almost 
microscopic figures with a crow-quill pen. Such fine work practically 
disappears on the blue-print. Figures, above everything else, should 
be bold and clear, since they cannot be guessed at. 

Erasing should be done very carefully with a sharp knife and hard 
rubber ; too much erasing wears a hole through the cloth. After 
erasing, the smooth surface must be restored before inking by rubbing 
with soapstone. Powdered pumice applied with the tip of the finger 
will remove ink from tracing-cloth without destroying the surface. 
If a bad mistake is made, it is sometimes possible to cut out a por- 
tion of the cloth and insert a new piece in its place, gluing the 
corners or edges. This can be done very neatly. 

Tracing-paper is often used, and is very satisfactory, though 
less durable than cloth. Water- proof ink is best for drawing on 
either. 

44. Blue Process Paper. Prepared paper for blue-prints can 
be purchased in rolls of different widths at such a low price and of 
such excellent quality that it hardly pays to prepare it for oneself, 
unless a large quantity of it is required. If it is. desirable, however, 
to make it, the chemicals may be used in the following proportions : 

1 oz. red prussiate of potash in 5 oz. water. 

1 oz. citrate of iron and ammonia in 5 oz. water. 



38 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



At time of use, mix and apply with soft sponge or broad, thin brush 
to one side of hard white paper. Keep the prepared paper in a dry, 
dark place until wanted for use ; it must be fresh to get the best re- 
sults ; with old paper the lines will be gray instead of white. The 
proportions of the chemicals in the blue-print mixture may be varied 
considerably without any effect, except to change the time required 
to print. 

In a bright, hot sun, from three to six minutes' exposure, according 
to the quality of the paper, should give a good copy. After printing, 
wash thoroughly in a sink of running water, letting each sheet remain 
in the bath a short time, if convenient. When it is required to make 
corrections or additions to a blue-print, a special preparation must be 
used to make white lines, and a solution of quick-lime and water, well 
shaken up, will be found satisfactory. To obliterate white lines or 
figures, go over them with a blue pencil. 

45. Miscellaneous Geometrical Constructions. (a) To Plot 
a Given Angle: Let it be required to draw a line <;, making an angle 
of x with ab (Fig. 14). On ab lay off any distance, as ad. At d erect 

a perpendicular, de, equal in length to 
oafxtan. x. Through e draw the line ac. 

If the angle x is greater than 45, plot 
aj_90 with the line af, using the same 
method. If the angle x is so large that 
the line tic is in one of the other three 
quadrants, plot the angle which ac makes 
with the nearest line (horizontal or verti- 
cal, as the case may be) through a. 

(b) To Draw a False Ellipse: When 
the difference between the major and 
minor axes of an ellipse is small, a close approximation to a true 
ellipse can be drawn with the compasses, describing four arcs, as fol- 
lows : 

(Fig. 15.) The distance from the centre of the ellipse to c is equal 
to the difference between the major and minor axes i. e., aa bb. 
The distance from the centre of the ellipse to c' is equal to three- 




14 ' 




fourths of aa lib. c, c, c', and c' will be the centres of the four arcs, 
each arc ending in the points n, as indicated in the figure. 

In ellipses too narrow for this method, 
find points on the ellipse by the method 
given in the next article ; draw end arcs 
and middle arcs as far as they can be 
drawn without deviating from the ellipse. 
(The centres of these arcs will be on the 
axes, and are found by trial.) Complete 
the ellipse by joining the arcs with the 
curve-ruler. 

(c) To Find Points on a True Elt /]> : 

Trammel Method. On a straight-edge (a calling-card will answer the 
purpose) mark off ed and ec, equal respectively to the semi -minor 
and semi-major axes of the ellipse. Move 
the straight-edge, keeping d on the major 
and e on the minor axis. The point c will 
move in an ellipse. A series of points can 
thus be obtained, through which the ellipse 
can be drawn with the curve-ruler or by 
any other method. 

(d) To Construct a Parabola : Let it be 
required to draw a parabola through the 

three points, a, 5, and c (Fig. 17). Draw cd and Id. Divide bd into 
any number of equal parts, 1, 2, 3, etc. Divide cd into the same 

number of equal parts, 1', 2', 
3', etc. Draw lines from c to 
1, 2, and 3. Intersect the line 
to 1 by a perpendicular from 
1', the line to 2 by a perpen- 
dicular from 2', and so on. 
Through the points thus ob- 
tained, draw half the parabola 
with the curve -ruler. Com- 
plete the other half by the same method. 




o o 




WOUKIXI; KNOWLEDGE 



(e) To Conxtriirt a If'/j i-ln>l,i : F'trxt M^tJimJ. In the left -band 
branch (.Fig. IS) let the curve pass through any point, as <-. and be 
symmetrical with respect to the two lines ah and In.: Draw any line 




through e, as <//<, g and A being on the lines <!> and <il> respectively. 
Lav off Iix = ij<' and ,/ will be on the hyperbola. 1'v drawing several 
lines through e, and laying off on each the distance from e to the near- 
est end of the line backwards from the other end, a series of points 
will be obtained through which the curve may be drawn with the 
curve-ruler. 

s, ,;,!!>/ M'tliml. In the right-hand branch (Fig. 18) / corresponds 
to e of the left-hand branch. Through /draw the horizontal linefk 
and the vertical line/*'. On//' mark off points 1, 2, 3, any convenient 
distance apart. Draw lines from I to 1, 2, and 3, and where these 
lines cross the vertical line through /draw horizontal lines. From 1 
drop a perpendicular to the upper horizontal line, from 2 to the next 
lower line, and so on. Through the points thus obtained draw half 
the curve, and complete the other half by a similar method, as indi- 
cated in the figure. 



CHAPTER IV 
ISOMETRIC PROJECTION AND CABINET PROJECTION 



46. A drawing in isometric projection or in cabinet projection 
represents an object approximately as it appears to the eye. These 
two projections are used as substitutes for true perspective to save 
time and labor. A drawing in perspective represents an object as it 
actually appears to the eye ; but in mechanical drawing this is not, 
as a rule, essential. An approximate outline in cabinet or isometric 
is more easily and quickly drawn, and will usually answer every pur- 
pose. 

ISOMETRIC PROJECTION 

47. FUNDAMENTAL PRINCIPLES. Isometric drawing is based on 
the following fundamental principles, as easily applied as they are 
remembered : 

(a) There are three lines called isometric axes (see Fig. 19). Thfy 
are a 30 line in one direction, a 30 line in ike other direction, and a 
vertical line. Thus these three lines, drawn from the same point, 

form a flat Y. 

,/' (o) The isometric axes represent 

^ 3o 1&' lines mutually perpendicular to each 

^^' other, and correspond to the three di- 

mensions, length, breadth, and height. 

A MEASUREMENT ON THE DRAWING CAN 
ONLY BE LAID OFF PARALLEL TO ONE 
OF THESE AXES. 



FIG. 19. ISOMETRIC AXES 



Measurements along a horizontal line, for 
example, are not made in isometric drawing. 




L= Length H= Height W= Width 



FIG. 20 



ISOMKTKIC PKoJKCTloN AND < A1UXKT l'U< UK< 'TK >N 



41 



ILLI-STKATION : In Fi>:. L'o there *iv six different views of the same block. 
In the two upper figures the height (II) is measured on a vertical line, the width 
(\V) uml the length (L) on 30 lines. 

(') In Fig. 20 the three figures on tlie right are simitar to the three on the left. 
Taking the figures in pairs, the only difference between two wliicli correspond is that 
in one case the Imti/ixt 30' lines extend lo the lift, wliile in the other they extend 
to the rif/fit. Hither inetliod is correct. When the length and width of an ohject are 
dinVrent. two such views can he drawn for each of its three positions, the draftsman 
choosing tlie one best suited to his purpose. 

(ll) Vll'til'lll lilllX ill till' Illljift (//'< I'l'l'fil-lll. lilliK ill tin I/I'll II'! III/. 

I. 'in, x Jlil/'it//,/ iii f/ii- i,lij,rf ,/,; j),i, ',///,/ iii. flu ili'ilir/lK/. It'illlit Hiiifli'x 

iii tli, uliju-f are HKHH/II/ , ilher G0 or / .' ,'tt, the drawing (see Fig. 20). 

48. Non-rectangular Objects. In drawing r<-<-litn</iiI<ir objects, 

the application of the foregoing principles is easy. Noiwectangular 

objects are also easily drawn in isometric ; but it takes more time, and 

the results as a rule are 
less satisfactory. The 
method is evident from 
. the following exam- 
ples : 

(a) First Method. 
ILLUSTRATION : Let it bo 
required to draw an iso- 
metric hexagon. First 

ilmw a true hexagon of the required size (Fig. 21). Draw a rectangle such that 
each of the six apices of the hexagon will be in a side of the rectangle. Draw 
this const ruction rectangle in isometric, and measure along its sides to locate the 
apices of the ixotm-lric hexagon, as indicated in the figure on the right (Fig. 21). 

(6) Any non- rectangular plane 

figure which can be inscribed in a ,'"*-. 

reel angle can be drawn in isometric 
in a similar manner. Any non-rec- 
tangular solid which can be inscribed 
in a rectangular block can be drawn 
in isometric by a method similar to 
that indicated in Fiir. 22. 

(c) Second Method. Let it 
be required to draw any irregular 
plane figure, as, for example, the 




Fi. 21 





one shown in Fig. 23. As this figure cannot be inscribed in a rectangle, draw 
any two co-ordinate axes, alt and ac. These axes can then be drawn in isometric, 
and each limiting point of the figure located by its co-ordinate distances, as indi- 
cated by the construction lines (Fig. 23). 




FIG. 22 



a i j 



Irregular solids can be drawn in a similar manner by using a third axis and a third 
ordinate. The three co-ordinate axes will correspond to the isometric axes. 

(d) The hexagon (Fig. 21) and the irregular figure (Fig. 23) have each been drawn 
in a horizontal plane. To draw them in a vertical plane, the rectangle in the first case 
and the co-ordinate axes in the second case should be drawn in the plane of a vertical 
and a huriznntid isometric axis, instead of in the plane of two horizontal isometric axes. 

49. Isometric Scale. An isometric projection of an object, if 
drawn to full scale, makes the object seem larger than it really is. To 
offset this, an "isometric scale" is sometimes used. Such a scale can 
be constructed as follows : Lay off true inches on a 45 line and drop 
vertical lines; these intercept isometric inches on a 30 line. Tlie 
inch may be subdivided in a similar way into 

as many parts as are necessary (Fig. 2-i). If 
the isometric scale be transferred to the edge 
of a strip of card-board it can be used like an 
ordinary scale. 

50. CIRCLES IN ISOMETRIC PROJECTION. To 
construct a circle in the upper face of the cube 
(drawn to isometric scale) of Fig. 25. Draw the diag- 
onals and the isometric lines m, m. The semi-major 
axis (ic (equal to the true diameter of the inscribed 
circle) can be measured equally on each side of c, with 

the regular scale of inches. Or it can be found graphically by dropping a perpen- 
dicular from r upon a 45 line through d; bc=ac is the semi-major axis. The 
ends of the minor axis n, n are found by drawing through a lines parallel to the 




Fir. 24 



42 



AX INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 25 



sides of the cube. The axes and four tangent 
points being known, the ellipse can be drawn 
by circular arcs and curve-ruler, or by any other 
method. 

If the cube is drawn to regular scale, the major 
axis of the ellipse will be longer than the actual 
diameter of the inscribed circle. The other direc- 
tions will remain true. The major axis can always 
be found by the construction of Fig. 25 given above. 
51. ISOMETRIC CIRCLE. A simpler way 
of drawing an isometric circle than that given 
in the preceding article is to find circular arcs 
to the ellipse without getting the axes at all. 
In Fig. 26 the ellipse is drawn from the four 
centres c, c', k, k'. To get centre k, lay off 

bk=bm. To get centre c, lay off cm =ab = to a side of the circumscribed square. 

This method applies to the use of any scale and is a close approximation. The 

ellipse is not exactly tangent to the sides at m, 

but the error is not perceptible. 

52. IRREGULAR CURVE. The method of 

drawing an irregular curve is illustrated in 

Fig. 27. The left-hand figure is the true 

shape of the upper and lower faces of a block. 

The right-hand figure is the isometric draw- 
ing of the same block, and the corresponding 

ordinates are marked with the same numbers, 

1, 2, 3, 4, 5. This method can be applied to a curve in space by using another 

ordinate. 







Fio. 27 



53. SHADOWS ix ISOMETRIC. The method of drawing shadows in isometric 
is illustrated in Fig. 28. The rays of light are 45 lines. The shadow in this 
case is on a horizontal plane through 

the base of the cross. To find shadow 
of the point a, draw a 45 degree line 
through the point and drop a perpen- 
dicular to a'. The intersection of the 
45 line through , and a horizontal 
line through ', gives the required 
shadow as. Shadows of other points 
are found in a similar way. Tlie 
work can often be shortened by re- 
membering that horizontal isometric 
lines have for their shadows lines 
parallel to themselves. Thus as <* is 
parallel to the corresponding isometric 
line ac. Shade lines representing edges, which cast shadows (see Art. 36), can 
usually be determined by inspection. 

For other examples of shade lines, see Fig. 20. 

CABINET PROJECTION 

54. (a) Cabinet projection is somewhat like isometric projection. 
The cabinet axes, however, are: A horizontal line, a vertical line, and 
a 45 line (see Fig. 29). All measurements on the 

drawing must be laid off parallel to these axes. .' 
Measurements parallel t<> the 4-~> axis /< In (If ax "/ 
long as tlie corresponding lines in the object. Verti- 
cal or horizontal measurements are laid off to full 
scale. 

ILLUSTRATION : In Fig. 30 there are six cabinet draw- 
ings of the same block in different positions. The dimen- 
sions of the block correspond to those of the block of Fie;. 
20. An opportunity is thus given to compare isometric 
and cabinet projections. In the figures here given the 45 edges arc marked 
their true length (L, II, or W, as the case may be), and not half this length 
(j, or "). They are drawn half length, however, according to the principle , 
given in Art. 54 (</). 



ISO. METRIC PROJECTION A\D CAI11NKT l'l;i >.JK< Tl< >\ 



(It). Il will lie seen from the 
figures that in cabinet as in iso- 
metric projection the draftsman 
has a choice between a left and 
a right hand view for any given 
position of a block. 

Can any additional views of 
the block (Fig. 80) be drawn V 

55. Rules for Cabi- 
net Projection. Tlic fol- 
lowing rules can be given 
for drawing in cabinet pro- 
jection : 

() /' / "" "'" /<"' f 
i.'i, <>lij, ii in. ur ]>nr<dlel to, 

111, jllilll: if ill: jIltjK T; t/lix 

a- ill l>f full x/'~i . i .i-iirt/ij like 

till fill' I itx> If. 

(/>} All lines perpendic- 
ular fa 1l n- front face will 
In '/-'i linix. Imlf ijii length 
vf corresponding Unix if tin- 
object. 

(C) To ll I'll If II, XO.N-K1 O 
TANUULAK Jlllt/lc JriJUIV, ill' KlG. 30 

i//i irrei/idur solid, in mlii- 

ni I jiroj'i-tiiin. nxe the methods of Arts, -is and 52. drawing the con- 
xtriictinn / ctangle, block, or co-ordiimti- <t,i-> x, iix the case may be, in cab- 
inet projection instead of isometric projection. 

56. CIRCLES IN CABINET PROJECTION. () Fig. 31 is the cabinet projec- 
tion of a cube with inscribed circles. The front face is full size, and the four 
edges perpendicular to it are 45 lines and half length. To construct a circle 
in the top face, draw the diagonals of the circumscribed parallelogram, and 
mark the four tangent points k\ k, h, h. To get points where the ellipse crosses 
the diagonals, draw perpendicular lines at m, TO, in the front face, to the 
upper edge, and then 45 lines meeting the diagonals at TO', in', m', m'. 
Thus, eight points on the ellipse are known, four tangent points and four 




L=LeKi g t(i, H-Height, W=Widtk 




FIB. 31 



points on the diagonals. The ellipse should lie 
sketched in pencil, and inked with the aid of 
a curve -ruler. This will require practice, but 
the draftsman should he able to construct a 
satisfactory ellipse in this way, without finding 
its axes. 

(Ii) A short way of finding the points where the 
ellipse crosses the diagonals is to make the dist.m., 
from the centre of the ellipse to in on the longer 
diagonal equal to one-half of hh, and draw a 45 line 
through each of the points thus found. This is an 
approximate method, but accurate enough for practi- 
cal purposes. It is not of much use to find axes, al- 
though it can be done without difficulty. The problem is recommended to the stu- 
dent as an exercise. 

(<) If additional points on the ellipse are required (which rarely occurs), 
the following method will give two such points in each quadrant: From a, 
one corner of the square, Fig. :5i>, draw lines to the middle of the opposite 
sides, m and n. Let b and b' be the middle points respectively of a n' and ,i m'. 

The intersection of b' n and a B is a point on 
the circle; the intersection of b m' and a m 
is another point on the circle. This is equal- 
ly true of the ellipse which represents a circle. 
By repeating this construction in each quad- 
rant, eight points of the ellipse can he ob- 
tained in addition to those found by the 
methods of the preceding articles. 

This method is geometrically correct, and 
applies to any form of oblique projection, to 
isometric and to perspective. 

57. Oblique Projection. Cab- 

Ti inet projection is one of several sys- 

FIG. 82 terns of oblique projection. Another 

sometimes used differs only in the length 

of the 45 lines, which are made full length instead of half length. 
This system is a trifle easier to execute than cabinet, but the appear- 
ance is usually less satisfactory. 




m 



m 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



58. () Isometric Projection 
pared. 

ISOMETRIC. 

Three axes parallel to which 
measurements corresponding to 
the three dimensions of space can 
be made. 

One axis vertical ; other two, 
30 lines to right and left. 

Measurements may be made to 
true or isometric scale, but which- 
ever scale is used it is the same 
for all isometric lines. 

No face of an object is drawn 
in its true shape and size. 




FIG. So ISOMETKIC CUBE 



and Cabinet Projection Com- 

CABINKT. 

Same. 



One axis vertical, one horizon- 
tal, one a 45 line. 

Measurements are full size on 
horizontal and vertical lines ; half 
size on 45 lines. 

The front face and others par- 
allel to it are drawn true shape 
and size. 




FIG. B4 CABINET CDBE 



In Fig. 33 the cube in full lines is drawn to isometric scale. The same cube drawn 
to full scale is represented by broken lines. It is seen that the cube drawn to isometric 
scale corresponds to the cabinet drawing of the same cube (Fig. 34), while that drawn 
true size appears much larger. 



As a rule, cabinet projection looks somewhat better, and is easier 
to execute than isometric projection. Each is especially adapted to 
the drawing of rectangular objects. Drawings of non- rectangular 
objects made in either of these two projections are usually unsatisfac- 
tory. Drawings to reduced or enlarged scale can be made in either 
projection. 

(b) ADVANTAGES AND DISADVANTAGES OF CABINET AND ISOMETKIC 
PROJECTIONS. The advantages and disadvantages of cabinet and iso- 
metric projections as compared with true perspective are: 

Advantages. (1) Time and labor saved. (2) Measurements can 
usually be scaled from the drawing itself. 

Disadvantages. (1) A picture drawn in isometric or cabinet is 
never a true picture. Linus which in perspective converge are paral- 
lel in isometric or cabinet; hence the drawing appears distorted and 
offends the eye. (2) One cannot choose the point of view from 
which to represent an object, as in perspective often a serious draw- 
back. 



CHAPTER V 



ORTHOGRAPHIC PROJECTION 



59. Projection. If from a point in space a straight line is drawn 
to a plane, the point in which the line meets the plane is &pr<>jt<-ti<>n 
of the point in space. The line itself is a_/'/\</Vr//'//y line. The plane 
is a plane of projection. 

60. ORTHOGRAPHIC PROJECTION. In Orthographic /'/'</< <-t!i>n : (a) 
A plane of projection is either a ;v litcal or a /H>/'/.:/I/</<// j>/ane. The 
planes of projection are assumed as transparent. 

(5) Every projecting line is perpendicular to the corresponding 
plane of projection. Hence projecting lines are either ltiiri:tnitl or i-fi-tiful lines. 

(c) The projection of a point on the vertical plane of projection is 
called its vertical projection ; its lt<iri::init<d />/'<>jir/ion is on the hori- 
zontal plane of projection. Hence horizontal projecting lines are used to rind 
vertical projections, and vertical projecting lines to find horizontal projections. 

ILLUSTRATION: In Fig. 36, pane 48, 1 represents a point in space. Iv rep- 
resents its vertical and In its horizontal projection. The dotted lines represent 
projecting lines. 

('/) A projection of a line may be found from the corresponding 
projections of its limiting points. 

A projection of a surface may be found from the corresponding 
projections of its limiting lines. 

A projection of a solid ma}' be found from the corresponding 
projections of its limiting surfaces. 

(e) In mechanical drawing, orthographic projection is used for the 
delineation of both the horizontal and the vertical projections of ma- 
terial objects upon two imaginary co-ordinate planes. 

61. ANGLES OF PROJECTION. () The two co-ordinate planes of 
projection (considered as infinite in extent) intersect at right angles, 



and thus form four rii/lit dint nil angles. Denoting the horizontal 
plane of projection by II and the vertical plane by V, a point, line, 
surface, or solid is said to lie in the : 

A IK/!, when it is above H and in front of V. 

.\injl, when it is above II and behind V. 
'I'lii I'd Amjl, when it is below II and behind V. 
Fourth Angle when it is below H and in front of V. 




FIG. 35 



46 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



In descriptive geometry (a higher and more extended study of or- 
thographic projection) all four angles are used. In mechanical draw- 
ing, however, the object is usually assumed as lying wholly within 
one angle, no attention being paid to the other three. 

(ft) The first angle is the one still used by many draftsmen for working drawings, 
but the third affords a more convenient arrangement of views (projections), and is more 
in accord with modern practice. The fundamental principles of drawing are practical- 
ly the same, no matter in which angle the object may be located, and a draftsman 
should be able to draw in any one of the four. Unless otherwise specified, the third 
angle will be used in all the problems of this course. 

(c) NOTE : The model shown in the photograph on the preceding page represents 
limited portions of the horizontal and vertical planes. The angles of projection formed 
by these planes are therefore limited. It should always be borne in mind, however, 
that the planes and angles of projection are in reality infinite in extent. 

The portion of the horizontal plane behind the intersection of the two planes and 
the portion of the vertical plane below this intersection are the planes of projection for 
an object in the third angle. Thus in this course little use is made of those portions of 
the planes containing the upper V and the left-hand H. 

(d) A portion of a third plane (called the end or side plane of projection) perpen- 
dicular lo the other two planes is shown in the photograph. If the portions of H and 
V not used for an object in the third angle be removed, the remaining portions of H and 
V. together with the end plane, correspond to the three transparent sides of the box of 
Fig. 36, page 48. The use of these planes of projections (including the end plane) will 
be explained in subsequent articles. 

62. VIEWS. (a) The projections of an object on H and V are 
called respectively its Horizontal Projection and Vertical Projection, 
or Plan and Elevation, or Top View and Front View. Of these three 
pairs of terms, Top View and Front View are to be preferred. They 
not only are definite, but they are also consistent with Bottom 
View, End View, Side View, or Rear View, terms commonly used 
in working drawings when the corresponding views of the object 
are shown. 

. (b) The projecting lines which determine any one view of an object 
are all parallel (since they are perpendicular to the same plane). These lines 
correspond to lines of sight ; but lines of sight never are parallel (since 
the eye never is an infinite distance away); hence a projection its never a true 
picture. The term view must therefore be used only in the sense of 
a projection. 

(c) REMARK : Unlike isometric and cabinet drawing, orthographic projection is 



not intended as a substitute for perspective. As a shadow may or may not resemble 
the object which casts it, so a projection may or may not look like the object pro- 
jected. Thus, at the outset, this form of drawing is unnatural, and the imagination 
must be trained to overcome the tendency of the eye to look for a picture instead of 
& prqfeotion. 

63. GROUND LINE. The line in which II and V intersect is called 
the (/round line. 

64. THE DRAWING. (a) To Represent the Planes of Projection: 
A horizontal line is drawn to represent the ground line. That portion 
of the paper above (or behind) this line represents one plane of pro- 
jection ; that portion of the paper below (or in front of) this line rep- 
resents the other plane of projection. 

The ground line may be drawn anywhere, its location depending upon the desired 
arrangement of the different views. 

H is in front of and V is above the ground line when the first angle is the one used. 

H is behind and V is below the ground line when the third angle is the one used. 

(b) The Relative Positions of Different Views : The positions of the 
different views (or projections) with respect to the ground line and to 
each other are the same as would result if one of the planes of pro- 
jection were revolved about the ground line until II and V are both 
in the same plane. 

ILLUSTBATION : In Fig. 36, let the top of the l>ox (which represents II) be 
revolved about the ground line until it is in the same plane witli the front of 
the box (which represents V). The relative positions of the views (Fig. 37) 
will now correspond to those in the drawing (Fig. 38). In (which is in H) 
is behind (above) and Iv (which is in Y) is below the ground line in both 
figures. 

(o) In orthographic projection, any point in the third angle has its 
top view (horizontal projection) behind and its front view (vertical 
projection) below the ground line. 

In using the third angle, it is well to accustom oneself to think of a top tinr us 
behind the ground line rather than above it. (Why ?) On tlie other hand, it is obvious- 
ly correct to speak of a front view as below the ground line. 

(d) Orthographic projection thus requires of the imagination two 
distinct processes: (1) To conceive each view on the corresponding 
plane of projection. (2) To determine the positions of the different 
views with respect to the ground line and to each other when the 
planes of projection have been brought into one plane. 



oUTIKHiUAl'IIIC 1'KOJECTJON 



47 



Eventually, as one becomes accustomed to this form of projection, he is less con- 
scious of any action of the imagination. As a matter of fact, an experienced drafts- 
man rarely thinks of the planes of projection at all, the different views of an object 
appearing to him as so many true pictures of it (although they are not). 

65. (a) To be able to draw in orthographic projection, one needs 
a working knowledge of a few of the fundamental principles of de- 
scriptive geometry. In the following articles these principles are 
given in the form of propositions for convenience of reference. I>y 
means of the photographs, however, they become self-evident. 

UEMAKK : The working knowledge above referred to is indispensable. The sooner 
one acquires it, the sooner the work of drafting becomes more truly mechanical. This 
does not mean that the propositions should be learned by heart, but that a thorough 
understanding of them helps the imagination, and guides the reason in working out any 
new problem which the draftsman may encounter. 

(b) In the photographs scattered throughout the remainder of the 
chapter, the glass sides of the box represent the planes of projection. 
(See Art. 61 d.) These photographs are intended to make clear how 
the views of a point, line, surface, or solid on the planes of projection 
are obtained. In many cases a second photograph shows the top 
glass (horizontal plane) revolved about the intersection of the top and 



front glasses (ground line) until the top and front glasses are in the 
same plane. This brings the views into the same relative positions 
that they occupy in the corresponding line drawing. Were it not for 
the perspective of the photograph, the views would be identical in out- 
line with those of the line drawing. It should be noted that a view 
on the top glass when it is horizontal is greatly distorted by the per- 
spective. Thus, in Figure 50, page 56, the view on the top glass is a 
true square, although it may not appear as such. In Figure 51 it is 
more nearly a square, because the upper glass was almost parallel to 
the plate in the camera when the photograph was taken. 

When the end plane is used, it is revolved about the intersection 
of the front and end planes (vertical ground line) until the end and 
front planes are in the same plane. This brings the end view oppo- 
site the front view. (See Figures, pages 58 and 59.) 

REMARK : The danger in the use of such photographs is in becoming too depend- 
ent upon them. It is evident that it is not necessary to imagine an object enclosed in 
a glass box in order to make an orthographic drawing of it, and the beginner iscautioned 
against allowing this to become a permanent habit. When the fundamental principles 
are thoroughly understood, the glass box should be discarded. (See Note Art. 64 d). 



48 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




IH 



'IV 



FIG. 36 



FIG. 



FIG. 38 



66. A POINT IN SPACE (Figs. 36, 37, 38). 

If In and Iv represent the top and front views respectively of the point 
1 in space, it follows : 

That the position of 1 is completely determined by these two views ; hence : 
( a ) Every point has two views (one on H. the other on V) by which 
its position in space is determined. 

That a plane can be passed through 1, IH, and Iv perpendicular to the ground 
line ; hence : 

(b) A point and its two views lie in the same plane perpendic- 
ular to both H and Vi. e., a plane passed through the two project- 
ing lines. 

That the distance from IH to the ground line is equal to the distance from 1 



to V. The distance of Iv from the ground line equals the distance of 1 from H; 
hence : 

(c) Tlie TOP VIEW of a point is as far BEHIND the ground line as the 
point itself is behind V. The FRONT VIEW of a point is as far BELOW 
the ground line as the point itself is below H. 

If a point Is equally distant from H and V, its two views will be equally distant 
from the ground line. 

That if the point 1 were no distance below H, 1 and IH would coincide, and 
Iv would be in the ground line. If 1 were no distance behind V, 1 and Iv 
would coincide and IH would be in the ground line; hence: 

(d) When a point lies in either H or V, one of its views coincides 
with the point itself, the other view will lie in the ground line. 



ORTHOGRAPHIC I'Uo.lrXTIoN 49 

A point lying in both H and V would coincide with both of its views in the ground (J) The /"'" ri< "'.s- of i/ point ill II-KI/X lie in the same straight line at 

l' ne - I'll/lit- idnjlix t<> flu- <jroiniil line. 

Tliis principle is continually used in finding one view of a point from the other 
THE DKAWIXi; HI- A POINT IX SP.U'K. vjew 

(c) ILM-STKATIOX: Assume the; point 1 (Fig. 36) to be 3" below II and 3J-" 

67. From Figures 37 and 38 it is evident that : behind V. Applying the principles of Articles 66 and 67 to the drawing 

(a) A point in space <'<i/i /t< /vy</v ///-*/ />// itx fn-n views, neither of (Fig. 38), In is 3J" behind the ground line. Iv is 3" below the ground line. 

///,/<// /'* tin poini itxt-lf. The line joining In and Iv is perpendicular to the ground line. 

A poini. line, surface, or solid never lias less than two views in true orthographic If 1 were no distance below If instead of a", where would Iv be ? 

projcciion Where must 1 be if both In and Iv are in the ground line? 



50 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




'I-2H 



4H 



3H 



IV 



2V 



FIG. 39 



FIG. 40 



FIG. 41 



68. STRAIGHT LINES. If 1 and 2 are the limiting points (ends) of 
any straight line 1-2 in space, the lines between IH and 2e, and be- 
tween Iv and 2v will be the top view and front view respectively of 
the line :U2. 

When the views of 1 and 2 on the same plane coincide, the corresponding view of 
1-2 will be a-point. 

69. STRAIGHT LINES PERPENDICULAR TO H OR V. 

In Figure 39, let 1-2 represent a line perpendicular to H and 3-4 a line 
perpendicular to V. It follows : 

That the point l-2a (Figs. 40, 41) is the top view of 1 and of 2, as -well as 
of every point in the line between 1 and 2. That, likewise, 3-4v is the front 
view of 3 and of 4, and of every point in the line 34. Hence : 



(a) A line perpendicular to either plane of projection has for its view 
on that plane simply a point. 

That the line Iv 2v is the front view of 1-2 (Art. 68). Since Iv and 2v 
are respectively as far from the ground line as 1 and 2 are from H (Art. 66 c), 
the line Iv 2v = l-2.' Since Iv 2v is parallel to 1-2, it is also perpendicular to 
the ground line. Likewise 3n4H = 3 |, and is perpendicular to the ground 
line. Hence : 

(b) A line perpendicular to either plane of projection has for its 
view on the. other plane a straight line perpendicular to the ground line, 
and equal in length to the line of which it is the projection. 

(c) If the line 1^2 is moved up until 1 is in H, Iv will be in the ground line (Art. 
66 d). If the line 3^4 is brought forward until 3 is in V, 3n will be in the ground line. 



1'KOJKCTION 



51 



Hence : If i>m n,d "f <i Ihic i In n'llirr /,lniii' 
r/, ir /,. tin 1 ntlii'l' l>lillli' irill li,' in tin' i/i-nilnil line. 



n, tl> n>ri'c*i><>iiiliii<j nn> <>f its 



THE DKA\VIX<: ( Ftynres 40, 4-1}. 

(</) li.i.rsTitATKiN : L.'t, the line Ui' (Ki<r. :{9) be 3" long, 3J-" behind V, 
upper end 1" below II. Then its top view (Fig. 41) will be the point 1-^n 



(Art. GO >/) ."?]-" behind the ground line. Its front view will be a line Iv 2v 3" 
Ionic (Art. 69 b) perpendicular to the ground line, Iv being 1" below it. 

If 3-4 is .3" long, 31" below II, and nearest end 1" behind V, its front view 
will be 3-4 v 3J" below the ground line ; its top view will be 8n 4n 3" long, SH 
n^ 1" liehind the ground line. 

If 1-2 were no (listnnre behind V, would 1-2 iiud Iv2v coincide? 



52 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




KiG. 42 



FIG. 43 



FIG. 44 



70. STRAIGHT LINES PARALLEL TO ONE PLANE OF PROJECTION BUT 
AT AN ANGLE WITH THE OTHER. 

In Figure 42 let 21 represent a line parallel to V but at an angle with H, 
and 3-4 a line parallel to H but at an angle with V. It follows : 

That 2n IH and 2v Iv (Figs. 43, 44) are, respectively, the top and front 
views of 2-1. Since 2-1 is parallel to V, 2v lv=2-l, and the angle which 
2v Iv makes with the ground line is equal to the angle which 2-1 makes with 
H. Likewise, 3n 4n = 3-4, and the angle 3n 4n makes with the ground line is 
equal to the angle which 3-4 makes with V. Hence : 

(a) When a line is parallel to either plane of projection, its 
view on tfiat plane represents the true length of the line ; and the 
angle which this view makes with the ground line is equal to the 



angle which the line in space makes with the plane to which it is 
not parallel. 

That since 2 and 1 are equal distances from V, 2n and IH are equal dis- 
tances from the ground line. Likewise, 3v and 4v are equal distances from the 
ground line. Hence: 

(5) A line parallel to either plane of projection has for its view on 
the other plane a line parallel to the ground line. 



That since 2 and 1 are not equal distances from H, 2n IH is shorter than 
2-1. Likewise, 3v 4v is shorter than 3-4. Hence : 

(c) When a line is not parallel to a plane of projection, its view on 
that plane is always shorter than the true length of the line. 



ORTHOGRAPHIC PROJECTION 53 



(r/) If a line lies in either plane of projection, it will coincide with its view on that view, L'V 1 v (Fig- 44), is 3" long find makes an angle of 60 with the ground 

plane. Where will its other view be 1 is, , Art. 09 c.\ line (Art. 70 </). The ])oint Iv is If below the ground line. Its top view, 

L'II In, is parallel to and :!]" lieliind the ground line (Art. 70 6). It is less than 

m , ,,. 1,111, 3 " l""ii' (Art. 70 c). Likewise, if 3-4 is 3" Ions;. 31" below II, makes an angle 

THE DWKO (Figure* /,, and U). of J ^ v ^ ^ 8 ._ lf( ^.^ ^ . ;{ is ^^ ^ 

(c) ILLI-STKATION : Let the line '2-\ (l''ii;. IL') Ke 3" lontr, ;: !j" I'diiml V, and makes an angle of 60 with the ground line. 3n is 1" behind the ground line, 

upper end 1 V below II. Let it be at an angle of 60 with H. Then its front 3v 4v is parallel to and 3J" below the ground line. 



54 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 45 



FIG. 46 



FIG. 47 



71. LINES PARALLEL TO BOTH H AND V, AND LINES PARALLEL TO 
NEITHER H NOE V. 

In Figure 45, let the line 1-2 be parallel to both H and V. It is evident 
then that both Iv 2v and IH 2n (Figs. 46 and 47) must both be parallel to 
the ground line. Hence : 

(a) A line parallel to loth H and V has for its two views lines par- 
allel to the ground line, both of which are equal in length to the line itself. 

If the two views of a line are parallel to and equal distances from the ground line, 
what position with respect to H and V does the line in space occupy ? 

In Figure 45, let the line 3-4 be parallel to neither H nor V. It is evident 
then that both 3v 4v and 3n 4a (Figs. 46 and 47) are shorter than 3-4 (Art. 
70 c). Moreover, the angle which 3v 4v makes with the ground line is not 



equal to the angle which 3-4 makes with H, although it is the front view of 
3-4 ; neither is the angle which 3n 4n makes with the ground line equal to the 
angle 3-4 makes with V. Hence : 

(5) If a line is parallel to neither plane of projection, both views are 
shorter than the line itself. The angles which the line makes with the 
planes of projection are not represented IN THEIR TRUE SIZE ly the angles 
which the views make with the ground line. 

(c) Any two lines, one in H and the other in V, drawn at random but having their 
corresponding ends in lines perpendicular to the ground line, will be the views of some 
line of definite length in space. 

(a!) A line of definite length at a fixed angle to either plane of projection may oc- 
cupy an infinite number of positions in space, but its view on that plane will always be 
of a constant length. 



ORTHOGRAPHIC PROJECTION 



ILLUSTRATION : Let a line 4" long at an angle of 60 with H be revolved about u 
vertical axis through any one of its points. In any one of its successive positions the 
line will make an angle of 60 with H (Why ?), and its top view will be 2" long. 
(Why?) 

72. PROFILE PLANE. A plane perpendicular to both H and V is 
called a jii'utfli plane. A line is in a profile plane when both of its views lie 
wholly within a line perpendicular 

to the ground line. 

73. GIVEN: The two 
/'/V//vs of a line, neither of 
which is parallel to the 
(i/'iiniiil line, to find the true 
l<-iii/th of the line and the 
angle it makes with either 




Fin. 48 



The line must be brought 
parallel to II or V (Art. 
TH "). For example, let it 
be brought parallel to V. 
Revolve the top view (al- 
lowing one of its ends to 
remain fixed) until it is 

parallel to the ground line. [This is equivalent to revolving the line itself 
(about a vertical axis through one of its ends) until it is parallel to V. (Why ?) (Art. 
70 *).] The corresponding front view will give the true length of the 
line, and the actual angle it makes with H. 

To find the angle the line makes with V, revolve the front vjew in 
a similar manner until it is parallel to the ground line. The corre- 
sponding top view not only gives the angle the line makes with V, but 
also the true length of the line, which should agree with that obtained 
by the first method. 



ILLUSTRATION: In Figure 49,let IH 2nand Iv2vbetlie views of aline in space. 
Revolve the top view about IH to the position IH 2H(n). (Why must the revolved 
position of the lop view be parallel to the ground line?) The point 2v moves in a 
line parallel to the ground line (Why?) until its revolved position 2v(n) is in a 
line through 2n(n) perpendicular to the ground line (Why?). Iv 2v(n) is the 



true length of the line \-->, and the angle X it makes with the ground line is 
equal to the angle 1-2 makes with II. 

If the front view Iv 2v be revolved in a similar manner until it is parallel 
to the ground line, the corresponding revolved position of In 2n will also give 
the true length of 1-2, as well as the angle it makes with V. (A check on the 
first method.) 

74. The converse of Article 73 is equally important. GIVEN: A 
line of definite length and the angles it makes with H and V, respec- 
tively, to Jind its two views. 




2H(R) 



I V s 




'2V(R) 



Fio. 49 



First draw the two views of the line when it is parallel to one 
plane of projection and at the given angle with the other. The shorter 
view must now be revolved (one end remaining fixed) to such a po- 
sition that the corresponding view on the other plane will be of the 
right length. (What will be this length ? One end of which view will move in a 
line parallel to the ground line during the revolution ?) 



56 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




4H 3H 




liH 2;H 



2iV 



I'v 



2V 



FIG. 50 



FIG. 51 



FIG-. 52 



75. PLANE FIGURES. A solid bounded by plane surfaces has for 
its edges straight lines, to any one of which the principles already 
given may be applied. When two or more edges are taken together 
additional principles pertaining to plane figures may be deduced. 

76. BOUNDARY-LINES AND SURFACES OF SOLIDS. 
From Figure 50 it is evident : 

That the two vertical edges of the square prism 11' and 2-2' have for front 
views two parallel lines. The top view of each is a point. 

That the two front views of 2-2' and 3-3' would be parallel if 3-3' were not 
directly behind 2-2', thus making the two front views coincident. Hence : 

(a) When two lines are parallel in space their corresponding views 
are parallel, unless these views are coincident or become mere points. 



If two lines in space intersect, their corresponding views will intersect, and a 
straight line between the two points of intersection will be perpendicular to the ground 
line. 

That the upper base 1234, beina; parallel to II, lias for a top view a square 
equal in size to the base itself. If the base were a hexagon or any other poly- 
gon parallel to H, the top view would be identical in outline with the base itself. 
Hence : 

(b) Any plane figure parallel to either plane of projection is pro- 
jected on that plane in its true outline. 

If the plane of an angle formed by two lines intersecting in space is parallel to 
neither H nor V, the views will always be greater or less than the angle they represent. 
Any plane figure must be brought parallel to either H or V to ascertain its true outline. 

That if the upper base is parallel to H its front viev.- will be a straight line, 



ORTI [OGRAPHIC PROJECT I ( ) N 



.-,7 



representing in reality four lines. Likewise, if the face 2 3 3' 1' is perpendicular 
to both H and V, its top and front views are both straight, lines. 

(c) When any plain fijn i'' is perpendicular to < itlni' ]>l<ni, <>t' !>,<>},<- 
tion its mew on that plane will lie a straight line. A j>lm ji<//i/; / /- 
pendicular to both planes of projection ha* fin' cadi <>f' its /'/'cws a 
xti'a'njlit line. 

77. SOLIDS. Mechanical drawing is mainly used to represent 
solids. But solids are bounded by surfaces, which in turn are bounded 
hv ////'. v, which are themselves limited by points. Views of a solid can 
therefore be found by drawing the views of its limiting points, lines, 
and surfaces, according to the principles already given. 

78. SQUARE PRISM. Let the prism (Fig. 50) be 2" square, 4" high. The 



upper base is parallel t<> and 1" below II. The front vertical face is parallel 
to and 2J" behind V. 

The top view of the prism (Fig. 52), therefore, is a 2" square, the front 
side of which is parallel to (Why '!} and 2^" behind (Why ?) the ground line. 
The front view is a 8" x 4" rectangle, the upper side of which is parallel to 
i \Vliy ?) and 1" below (Why ?) the ground line. 

79. A.SSOIINC; THE POSITION OF AN OBJECT. The prism (Fig. 50) is in such 
a position, with two faces parallel to V and two bases parallel to H, that the top and 
front views are very simple. The draftsman usually assumes the faces of the object 
which he particularly wishes to show parallel to H or V. This, however, is often im- 
possible. Solids are therefore purposely assumed at angles with H and V in many 
problems in order that the student may learn to represent an object in any position 
whatever. (See Arts. 83. 84.) 




58 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 53 



FIG. 54 



Fio. 55 



80. ADDITIONAL YIEWS. It often happens that the top and front 
views of an object in a given position do not adequately represent 
it. For example, the top and front views of a square prism in the 
position shown in Figure 53 are both rectangles. But the top and 
front views of the cylinder, Figure 56, are also two similar rectan- 
gles. The ends of the rectangles in one case represent squares, in 
the other case circles, but there is nothing to show this. Something 
more is needed, then, to determine whether the rectangles them- 
selves are views of a square prism or of a cylinder. Accordingly, end 
views are shown (in Figure 55 a square, in Figure 58 a circle) which 
remove all doubt. 



81. (a) THE PRISM, FIGURE 53. 

Let the prism (Fig. 53) be 2" square, 4" long, with its top face parallel to and 
2" below II, its front face parallel to and 2J" behind V, and its end 2" from 
E (the end plane of projection). The top and front views are obtained in the 
usual manner. The -end view is obtained in precisely the same way as the other two 
views, except that V and E are used instead of H and V. This view will there- 
fore be a 2" square, since the end of the prism is parallel to E. The end plane 
is revolved about its intersection with V (a vertical ground line) when the three 
pla'nes are brought into one, as shown in Figure 54. In Figure 55 the end view 
will therefore be projected across (horizontally) from the front view, and the clear 
space between the two views will be 24/'+2"=:4J". If a vertical ground line 
is drawn, it will be 2" from the front view and 2^" from the end view. (Why ?) 



ORTHOGRAPHIC PROJECTION 



59 




FIG. 56 



Fie. 57 



Fio. 58 



(5) THE CYLINDER, FIGURE 56. 

Let the cylinder (Fig. 56) be 2" in diameter and 4" long, with its axis paral- 
lel to and 3" from both H and V. The end of the cylinder is 2" from E. 
The end view (Fig. 58) is a circle, the centre of which is on a horizontal line 
through the centre of the rectangle (front view) and 2" + 3^";=5J" away from 
the end of this rectangle. (Why ?) 



(c) In general : The front and end mews of any point lie in the same 
horizontal line i. e., a line at right angles to a vertical ground line. In 
a similar way all the principles relating to points and lines when H 
and V are used can be easily modified to apply to V and E or H and E. 

It is often more consistent to call the view on E a side view instead of end view. 
(See Art. 84.) 



60 



AN INTRODUCTORY COURSE IN MECHANICAL 




(d) THE HEXAGONAL PKISM, FIGURE 59. 

The hexagonal prism (Fig. 59) is another illustra- 
tion of the necessity of adding an end view. In the 
orthographic drawing (Fig. 60) the end view is drawn 
first in its proper position and the other two views 
derived from it as indicated. 



Fio. 59 



FIG. 60 



82. THE HEXAGONAL PYRAMID, FIGUKE 61. 

Let the pyramid (Fig. 61) have its base parallel to H. Let its altitude be 
4" and a side of the base 1" long. The top view of the pyramid (Fig. 62) will 
be a true hexagon, one side of which is 1" long (Art. 76 b). The diagonals of 
this hexagon should not be thought of as diagonals at all, but as views of edges 
which run from the vertex to each corner of the base. In the front view the 
base is represented by a straight line (Art. 76 c). Since the altitude of the 
pyramid is parallel to V, its true length, 4", can be measured above the centre 
of the base, in the front view, to find the point representing the vertex. 




FIG. 61 



FIG. 62 



ORTilOGIi A PI! 1C PROJ ECTIO N 



61 



83. INVISIBLE EDGES. When a portion of a solid is 
between one of its edges and a plane of projection, the 
view of the edge on that plane is invisible. Invisible 
edges are represented by broken lines. (See Art. 
32 .) 

ILLUSTRATION : The prism (Fig. 63) has been so placed with 
ivspuct to V that the rear edges are not directly behind the 
front edges. One of these rear edges is visible in the front 
view, the other is invisible and is represented by a broken line. 
In the side view the edge farthest from E is invisible. 

Invisible edges are usually shown when the drawing is ina.de 
clearer thereby, otherwise they may lie omitted. 

84. THE SQUARE PEISM OF FIGURE f>3. 

Let the prism of Figure 50 be turned until the front face, 
instead of being parallel to V, makes an angle of say 30 with 
A' (Fig. 63). The dotted lines (which are in reality projecting 
I'mrx) indicate how the front and side views can be derived from the top view. 
In the orthographic drawing (Fig. 64) it is therefore necessary to draw the top 
view first. This top view will be a square, since the base of the prism is still 
parallel to H, but the side of the square which represents the top view of 
the front face (Art. 76 c) makes an angle of 30 with the ground-line. (Why?) 
The nearest corner of the square is as far behind the ground line as the near- 
est edtre of the prism is behind V. (Why?) The front view of any point or 
edge can be found by drawing a line at right angles to the ground line through 
the top view of the same point or edge (Why?), and laying off on this line 
the proper measurements below the ground line. (What will the proper measure- 
ments correspond to?) The work is indicated by the projecting lines (Fig. 64). 

REMARK : When in doubt as to which view of an object to draw first, select that 
one which shows a base, face, or end of the object in its true outline, i.e., the view on 
that plane of projection to which part of the object is parallel. 

85. A SOLID INCLINED TO H AND V. (a) When a solid is inclined 
to both H and V, it is in the most difficult position to draw in which 
it is possible to place it. The process consists of three steps : (1) The 




FIG. 63 



FIG. 64 



solid is assumed in some simple position with respect to II and V, and 
a drawing made of it in this position. (2) The solid is tipped with 
respect to one plane, but its position with respect to the other plane 
remains unchanged. (3) The solid is tipped with respect to the plane 
to which it has not yet been inclined, but its position with respect to 
the other plane is the same as it was at the end of the second step of 
the process. The views of the solid in this third position are the ones 
required. These views are, in part, derived from those of the second 
step, which are in turn derived from the views of the solid in its first 
position. 

NOTE : To avoid confusion, it is well to assume that each time the solid is tipped 
it is also moved far enough to the right or left to enable a separate pair of views to be 
drawn for each of its three positions. (See page 62.) This is not essential, however, 
for the three pairs of views can be drawn in the same place on the paper, the views of 
the solid in its first two positions serving as so many construction lines which may be 
afterwards erased. The latter arrangement is often made necessary by the limited 
amount of space available. The method of determining the views is practically the 
same, no matter which arrangement is adopted. 



62 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 68 



Km. 70 



ORTHOGRAPHIC PROJECTION 



63 



(5) ILLUSTRATION : SQUARE PRISM INCLINED TO H AND V. 

FIRST POSITION. 

The position of the prism with respect to II and V in Figure 65 is the 
same as. that of Figure 63, page 61. Hence the corresponding orthographic 
drawing Figure 68 is exactly like that of Figure 64, page 61, except the side 
view has been omitted. 

SECOND POSITION. 

In Figure 66 the prism is tipped up until the plane of the upper base makes 
an angle with II (any desired angle), but the position of the prism with respect 
to V IMS not been changed; that is, every point of the prism is just as far be- 
hind V in Figure 66 as it is in Figure 65. Hence : (1) The front view (Fig. 69) 
is the same in outline as the front view of Figure 68, but it is tipped until the 
upper line makes the same angle with the ground line that the plane of the 
upper base makes with II. 

(2) Since in tipping the prism (and moving it to the right) every point of 
it was moved parallel to V, the top view of any particular point is as far behind 
the ground line in Figure 69 as in Figure 68 i. e., its path during the change 
of position of the prism was a line parallel to the ground line. 

(c) The actual work of drawing is as follows: (1) At any convenient dis- 
tance to the right, copy the front view of Figure 68, but incline it at the de- 
sired angle to the ground line. (See 1, above.) In this case the line Iv 4v 2v 3v, 
representing the front view of the upper base, is drawn at 30 to the ground 
line, since the upper base makes an angle of 30 with H. 

(2) Through the principal points in the top view of Figure 68, draw lines 
to the right parallel to the ground line. The corresponding points in the top 
view, Figure 69, will lie somewhere in these lines. (See 2, above.) 

(3) Through any point in the front view of Figure 69, as 3v, draw a line at 
right angles to the ground line. The point 3n (Fig. 69) will be at the inter- 
section of this line and the line parallel to the ground line through 3n (Fig. 
68). In a similar manner draw lines perpendicular to the ground line through 
each of the principal points of the front view (Fig. 69), and find the inter- 
section of each of these lines with the line through the corresponding point of 
the top view (Fig. 68) parallel to the ground line. 

(4) Between the points thus found draw (1) all the visible edges, and then 
(2) the invisible edges, if they are to be shown. 

(d) In more complicated figures it is difficult to connect the proper points in the 
top view unless the}' have been systematically kept track of. It will save time to num- 



ber or letter the principal points of the first figure and use the same notation for the 
corresponding points in the second figure, marking each jwint UK mum n fm/ml. For 
example, if the corners of the upper base (top view, Fig. 68) are lettered around in 
order la, 2n, 3H, and 4n then In. 2n, 8n, and 4n of tlie new top view (Fig. 69) 
may be joined in order, and these lines, being in the upper base, will all be visible. 
The corners of the lower base should be distinguished in some way from those of the 
upper base. A good way is to let 1' lie the corner under 1, 2' under 2, and so cm. us 
shown in thu figure. Then I'H, 2'n, 3'H, aud 4'n can be joined in order, but 2 H 3 n 
and ;i ii 4' n will be invisible. Likewise, corresponding points of the upper and lower 
bases, as In and l'n, 2n and 2'H, etc., may be joined, since these lines will represent 
the top views of the corresponding edges. 

() All lines in the perimeter of any top view are always visible. These can be 
drawn first. A line within this perimeter is invisible when from the frout view it is 
seen to be underneath any portion of the solid (Art. 83). 

THIRD OR FINAL POSITION. 

(/") The position of the prism Figure 67 with respect to H is the same as 
that of the prism Figure 66. The vertical edges, however, instead of being 
parallel to V, are now inclined to V. Note that : 

(1) The top view (Fig. 70) must be the same in outline as the top view 
of Figure 69. (Why?) 

(2) Every point in the new front view (Fig. 70) must be as far below the 
ground line as the corresponding point in the front view Figure 69. (Why?) 

(y) The actual work of drawing is as follows: (1) At any convenient dis- 
tance to the right, copy the top view of Figure 69, but incline it at the desired 
angle to the ground line. [If in the final position of the prism a vertical edge makes 
an angle say of say 60 with V, how can one find the angle which the line representing 
this edge in the top view makes with the ground line.] (See Art. 74.) 

(2) Through the principal points in the front view (Fig. 69) draw lines 
parallel to the ground line. (Why?) 

(3) Draw lines through each of the principal points of the top view (Fig. 70) 
perpendicular to the ground line, and find the intersection of each of these lines 
with a line through the corresponding point of the front view (Fig. 69) par- 
allel to the ground line. [For example, a line through 3n (Fig. 70) perpendicular 
to the ground line intersects a line parallel to the ground line through what point of 
the front view ?] (Fig. 69). 

(4) Between the points thus found draw (1) the visible and (2) the invisible 

edges. 

(h) All lines in the perimeter of the new front view are visible. A line within this 
perimeter is invisible when from the top view it is seen to lie behind any portion of the solid. 



64 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 71 



Fio. 72 








Fui. 74 



FIG. 7.1 



ORTHOGRAPHIC PROJECTION' 



65 



(&) ILLUSTRATION : HEXAGONAL PRISM INCLINED TO H AND V. 

A solid may be tipped first with respect to V and then with respect to H. 
The final result will be the same, no matter to which piano the solid is first 
inclined. In Figures 71 and 74, for example, a hexagonal prism has its axis 
parallel to both II and V. In Figures 72 and 75 this axis has been inclined 
to V (instead of II), but it is still parallel to II. The top view of the prism 
is therefore the same as before, except that it is turned with respect to the 
ground line. The new front view, Figure 75, however, must be derived from 
the front view, Figure 74, and the top view, Figure 75. 

The third and final position of the prism is shown in Figures 73 and 7ti. 
Here the front view is the same in outline as in Figure 75, the position of the 
prism with respect to V not having been changed from that of Figure 75. 
The axis of the prism, however, is now inclined to H ; hence the new 



top view, Figure 76, must be derived from the top view, Figure 75, and 
the front view, Figure 76. In the figures referred to, a single point of 
the prism can be traced through the different steps of the process by means 
of the broken construction lines. Invisible edges are purposely omitted in 
the drawing. 

No matter how complicated the position of an object with respect 
to the planes of projection may be, by assuming the object in a simple 
position, and then tipping it tirst with respect to one plane and then 
the other, according to the process just described, the two views of 
the object are easily found. It requires considerable care, however, in 
projecting points from one figure to another if extreme accuracy is to 
be attained. 



66 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 77 



FIG. 78 



FIG. 79 





FIG. 80 



FIG. 81 



FIG. 82 



ORTHOGRAPHIC PROJECTION 



67 



\ 



\ 



\ 



FIG. 85 



FIG. 86 



FIG. 87 



Fin. 88 



86. I'r.AXEs. The line in which any plane intersects II is called 
the horizontal tmc<> of that plane ; its vertical trace is the line in which 
it intersects V. 

From the figures it is evident that : 

A plane parallel to either II or V has but one trace, and that 
tr;..cr is parallel to the ground line (Figs. 77, 78, 83, 84). 

(6) When a plane is parallel to the ground line its traces are paral- 
lel to the ground line (Figs. 79, 85). If a plane is not parallel to tbe ground 
line and has two traces, these traces will meet in the ground line. (Why?) 

(c) A plane perpendicular to H has its vertical trace perpendicular 
to the ground line (Figs. 80, 86). The horizontal trace of a plane per- 
pendicular to V is perpendicular to the ground line (Figs. 81, 87). 



(d) If a plane is perpendicular to H, but makes an angle with V, 
this angle is equal to the angle made by the horizontal trace with the 
ground line (Figs. 80, 86). If a plane is perpendicular to V, but makes 
an angle with II, this angle is equal to that between the vertical trace 
and the ground line (Figs. 81, 87). 

(e) Each of the traces of a plane oblique to both H and V is at an 
angle with the ground line, but the angles thus shown are not equal 
to the angles which the plane makes with H and V (Figs. 82, 88). 

(f) A plane perpendicular to both II and V is called a profile 
plane ; its traces lie in the same straight line perpendicular to the 
ground line (Fig. 48, page 55). 

A trace of a plane is represented by a dot and a dash alternating. (See Art. 32 d.) 



CHAPTER VI 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 
SURFACES OF REVOLUTION, PLANE SECTIONS, INTERSECTIONS, AND SHADOWS 



87. A CIRCLE INCLINED TO H AND V. (a) When the plane of a 
circle of x inches diameter is parallel to a plane of projection, its view 
on that plane is a circle x inches in diameter. Its view on the other 
plane is a straight line parallel to the ground line (Art. 76 J, c). 

(b) When the plane of a circle is not parallel or perpendicular to a 
plane of projection, its view on that plane is an ellipse. 

(c) Let it be required to find the views of a circle, the plane of 
which is neither parallel nor perpendicular to H or VY 

first Method. (1) Assume the circle parallel to one of the planes 
of projection, and draw the top and front views of it in this position. 
(2) Keep it perpendicular to one plane, but incline it to the other, and 
find the new top and front views (second step, Art. 85). (3) Incline 
the plane of the circle to the plane of projection, to which it has been 
kept perpendicular in (1) and (2) (third step, Art. 85). 

ILLUSTRATION: (1) Assume the circle Figure 89 parallel to II. Its top view 
is a circle. Its front view is a straight line. On the circumference of the circle 
assume any number of points. (These points may be assumed, for example, 
about 30 of arc apart. Each point will have two views, which may be num- 
bered and lettered in the usual way.) 

(2) In Figure 90 the circle has been kept perpendicular to V, but inclined to 
H. The points in the new top view (Fig. 90) corresponding to the points as- 
sumed in Figure 89 are easily found by the method explained in the second step 
of the process (Art. 85). This new' top view will be an ellipse (Art. 87 4), 
plotted by means of the points just found. 

(3) In Figure 91 the angle which the plane of the circle makes with H is the 
same as in Figure 90, but it has now been inclined to V. The new top view (Fig. 





3V 



- 

3V(R) 



FIG. 89 



FIG. 90 



FIG. 91 



91) is exactly like the top view of Figure 90, but turned with respect to the ground 
line. (The angle which the major axis, for example, makes with the ground 
line depends on the angle which the plane of the circle makes with V.) The 
new front view (Fig. 91) is an ellipse found by points derived from correspond- 
ing points in the front view (Fig. 90) and the top view (Fig. 91) (third step, 
Art. 85). 

REMARK : This method is general, and may be applied to any curve or irregular 
figure. Note that the major axis of an ellipse which is a view of a circle, is always 
equal in length to the diameter of the circle. (Why?) 



SPECIAL APPLICATIONS OF OKTIIoCKAl'IIH' PROJECTION 



^ \ond M> I/in,!. -In the case of a circle, a much shorter method 
than that given above is to assume but four points in a ligure such 
that thr corresponding points of the succeeding figure will be the 
ends of the major and minor axes of the required ellipse. 

ILLUSTRATION : The ends of tin- axes in tlic top view (Fig. 90) correspond 
respectively to the extreme top and bottom points and the extreme left and 
right points of the circle (top view, Fig. 89). To find the axes of the ellipse in 
the front view (Fiir. 91) is more difficult. Tin; method is as follows: The line 
In 2n (Fig. 91) is tl'e top view of that particular diameter of the circle which 
is parallel to V. (\VliyV) Hence the corresponding front view Iv 2v (Fig. 91) 
will equal the true length of the diameter of the circle. Iv 2v is the major 
axis of the ellipse. To find the points Iv and 2v (Fig. 91), find by measure- 
ment In ami 2n (Fig. 90), then Iv and 2v (Fig. 90), and project across from 
the front view (Fig. 90) and down from the top view (Fig. 91), as indicated. 

The ends of the minor axis 3v and 4v (Fig. 91) are found as follows: In 
the front view (Fig. 90) revolve the circle about a diameter parallel to V until 
the circle is parallel to V. The broken circle is the view of the circle in this 
position. The point 2v will move to 2v(it). (Why?) The point 3v(n) is 90 
of arc from 2v(n). Revolve the circle back and 3v(n) moves to 3v. 3v is 90 
from 2v, and hence must be one end of that particular diameter of the circle 
perpendicular to the diameter 1-2. Hence if 3v is projected across to the 
front view (Fig. 91) on to a line perpendicular to and bisecting Iv 2v (Fig. 91), 
the new ;iv (Fig. 91) is an end of the minor axis. 4v is an equal distance the 
otl.er side of the intersection of the two axes. 

88. SURFACES OF REVOLUTION. The views of a cylinder, the axis 
of which is perpendicular to II or V, are a circle and a rectangle. 

The views of a cone, the axis of which is perpendicular to H or V, 
an- ;i circle and a triangle. 

If the axis of a cylinder or cone is parallel to neither H nor V, n circular base is 
projected in an ellipse (Art. S7i. 

Cylinders, cones, and other similar solids nre assumed as right solids, unless it. is 

otherwise specified. 

Any view of a sphere is a circle equal in diameter to a great circle 
of the sphere. 

89. Given : One view of a point on a surface of revolution to 

tli, <it In /' I'ii W. 




09 



aH 



(") General Method : Every point in a surface of revolution must 
lie in some one element (straight line or a circle) of that surface. Let 
the top view of a point be given. Through this view draw a top view 
of the element in which the point lies. Find the front view of the 
same element. The front view of the given point will lie in the front 
view of the element, and the line joining the two views of the point 
must be perpendicular to the ground line (Art. 67 I). 

If the front view of a point wen; given, how would the top view be found ? 

(4) ILLUSTRATION : Cylinder. Let 
IH (Fig. 92) be the top view of a point 
1 on the surface of a cylinder. Re- 
quired Iv. 2H 3n is the top view of 
the element through the point 1. This 
element intersects the circumference 
of the right-hand base in SH. The cir- 
cumference appears as a straight line, 
but if it is revolved to the position in- 
dicated by the broken circle, 3n will 
move to 3'. It is now seen that the 
element intersects the circumference a 
distance X above the horizontal diam- 
eter aa, of which OH an is the top 
view and the point aav the front view. 
Therefore 3v must be a distance X above aav on the front view of the circum- 
ference. 2v 3v is then the front view of the element, and Iv, the required 
view, is on 2v 3v, as indicated in the figure. 

The line 2n 3n is also the top view of another element directly beneath 2-3, and as 
far below the diameter aa as 2-3 is above it. In could therefore be the top view of an- 
other point, of which 1'v is the front view. 

QUESTION : How would the top view In be found -if the front view Iv were given ? 

ILLUSTRATION: Cone. Let Iv be the front view of a point 1 on the surface 
of a cone. Required IH. 

(c) First Method (Fig. 93) : The cone can be conceived as made up of an 
infinite number of circles, from one of zero diameter at the vertex to one of 
aa diameter at the base. The particular circumference in which the point 1 
must lie is of the diameter b!>. The top view of this circle is found as indi- 
cated, and 1 H is the required point. 





~\ 








\ 




I 


2hf JH 3H 


<-X~<i/. 




/ 


c 


g 











2V IV 3V 






X 


a 


aV 


* 





Flf . 92 



70 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 





V 






3V 




FIG 93 



FIG. 94 



FIG. 95 



(d) Second Method (Fig. 94): The front view of the particular element of 
the cone in which 1 must lie is 2v 3v. The top view of this element is found 
as indicated in the figure, the position of IH is then evident. 

QUESTION : How would Iv be found if IH were given in either of the above ex- 
amples ? 

Iv is tlie front view of another point on the surface of the cone directly behind 1, 
the top view of which is I'H (Fig. 93). 

(e) ILLUSTRATION : Sphere (Fig. 69). Let IH be the top view of a point on 
the surface of a sphere. Required Iv. The sphere can be conceived as made 
up of an infinite number of circles, increasing from zero diameter in front to the 
diameter of the sphere at the centre, and decreasing to zero diameter again at 
the extreme rear. The diameter of the particular circumference in which the 
point 1 must lie is equal to aa. There can be only one circle of this diam- 
eter in the front view, and Iv must be on its circumference, as shown in the 
figure. 

IH is the top view of another point on the surface of the sphere directly beneath 1. 
1'v is the front view of this point. 

Solve the problem by conceiving the circles of different diameters, all perpendic- 
ular to the vertical axis of the sphere. 

Find In when Iv is given. 



PLANE SECTIONS. 

90. When an object is cut by an imaginary plane and the 
portion cut is shown in a separate view, the latter is called a 
section view. 

Section views are useful in showing the invisible pints of an object when broken 
lines fail to make the drawing clear. For example: a hollow object having something 
within which it is necessary to show can be conceived as cut in two by a piano, and part 
of the shell removed, leaving the interior in full view. Section views are often drawn 
in place of an end, side, top, or bot- 
tom view. The portion of the object 
cut should be section -lined. (See 
Art. 39.) 

ILLUSTRATION: The section view 
of a box (Fig. 96) shows how the 
bottom of the box is set into the 
sides and how the top laps over. 
This would be shown in an end 
view, but not quite as clearly. The 
cutting-plane was assumed parallel 
to the end of the box. 



1 



FIG 96 



91. CYLINDER. Axis Parallel to H and V ; Cuttiny-plane Parallel to V 
(Figs. 97, 98). 

The plane is assumed a distance b in front of the axis of the cylinder. It 
cuts from the surface of the cylinder two elements, the top views of which are 
both represented by the line aa. The front views of the same elements are 
found as in Article 89 b. That portion of the cylinder between these front 
views is the true section cut by the plane. 

Find section cut by a plane parallel to H a distance b above ihe axis. 

92. CYLINDER. Axis Perpendicular to H ; Cutting-plane Parallel to V 
(Figs. 99, 100). 

The plane cuts the circumference of the circle in the top view in two points, 
a and a. The space between the front views of the corresponding elements 
cut from the surface of the cylinder is the true section cut by the plane. 

The plane was assumed a distance b in front of the axis. How would the section 
be found if the axis of the cylinder were perpendicular to V and the cutt-ing plane 
parallel to H, a distance b above the axis? 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



71 




KM.. '.17 




FIG. 98 

93. SPHERE. Cut l>y a Plane Parallel 
to V (Figs. 101, 102). 

Assume the plane a distance b in front 
of the centre of the sphere. It cuts from 
the sphere a circle, the top view of which 
is a straight line, act. The front view of this 
circle is easily found (Art. 89 ), and the 
space within is the true section cut by 
plane. 





FIG. 101 



FIG. 99 






FIG. 100 



FIG. 102 



Find section cut from 
the sphere by a plane par- 
allel to H, a distance b 
above the centre of the 
sphere. 

94. SPHERE. Cut 
by a Plane Perpendicu- 
lar to H, at an Awjle 
of X with V (Art. 86 d) 
and a Distance b from 
the Centre of the Sphere. 
(Figs. 103, 104). 

Whatever the curve 
cut from the surface of 
the sphere may be, its 
top view is the straight 
line aa. Let In be any 
point in aa. Then Iv 
is easily found, since 1 
is on the surface of the 
sphere (Art. 89 ). By 
assuming several such 



72 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




Fio. 103 





FIG. 104 



points in aa and finding the correspond- 
ing front views, the front view of the 
section itself can be drawn. This 
front view is an ellipse, but the true 
section cut is a circle. 

A shorter method is to find the four 
points in the front view, which are the ends 
of the major aud minor axes, and construct 
the ellipse by one of the methods of Article 
45. 

95. SQUARE PRISM. Base Par- 
allel to H ; Cutting - plane Perpendicu- 
lar to V, at Angle of X to H (Figs. 
105, 106). 

The plane is located by its traces 
(Art. 86 d). If the portion of the 
prism above the cutting - plane is re- 
moved, the top view (Fig. 106) shows 
the section cut, but not in its true size 
or shape, for the plane of the section 
is not parallel to H or V. 

If the section is revolved until it 
is parallel to a plane of projection, it 
will be shown in its true outline. This 
is the usual way of showing such a 
section. In Figure 106 the section lias 
been revolved until it is parallel to V. 
The view thus obtained is placed any 
convenient distance to one side of the 
front view of the prism. 

96. CYLINDER. Axis Perpendicu- 
lar to V ; Cutting-plane Perpendicular 
to H, at an Angle of X with V (Figs. 
107, 108). 

The method is similar to that of 
the preceding article. The section cut 
is an ellipse, the major axis of which 



is equal in length to mi, 
and the minor axis to the 
diameter of the circle. 
(Why?) If any other point 
on the ellipse, as 1', is re- 
quired, it is found as in- 
dicated in the figure. 

Find section cut from a 
cylinder, the nxis of which is 
vertical. Cutting-plane per- 
pendicular to V, at an angle 
with H. 

97. CYLINDER. Asix 

Perpendicular to H, Cut- 

tinij-plane Parallel to the 

Ground Line (Figs. 109, 

110). 

Let the plane be given 
by its traces XH and Xv 
(Art. 86 b). Revolve the 
cylinder on its axis one 
quarter way round, and let 
the cutting -plane be re- 
volved with it ; the latter 
now becomes perpendicular 
to V, and its traces in its 
revolved position are XH(R) 
and XV(R). The ellipse 
can now be drawn as in 
the preceding article, and 
the cylinder revolved back 
to its original position. 

CONIC SECTIONS. 

98. (a) HYPERBOLA. 
In Figure 112 the axis 
of the cone is vertical. 




FIG. 105 





\ 




Fio. 106 



si-l-X'IAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 




of points is obtained through which the curve can be drawn. Tin's gives 
the Intf (\Vliy?) outline of the section cut from the cone. It is a hyperbola. 



FIG. 107 




FIG. 108 

The cutting-plane is parallel to V, a distance b in front of the axis. The hor- 
izontal trace of the plane is shown in the top view (Fig. 11 L>). Whatever the 
curve cut from the surface of the cone may be, the top view of it is the straight 
line, aa. Tt remains to find the front view of the curve. Let the point 1, 
of which In is the top view, be any point in the curve. If 1 is in the curve, 
it must lie on the surface of the cone, and IH being assumed, Iv can be found 
as in Article 89 c or 89 d. By assuming a number of points in the top view 
of the curve and finding the corresponding points in the front view, a series 




FIG. 109 




74 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIB. ill 





FIG. 112 



The top view of the highest 
point of the curve will be direct- 
ly in front of the centre of the 
circle. (Why ?) 

(6) PARABOLA. 

In Figure 114 the cutting- 
plane is perpendicular to V and 
parallel to the extreme left-hand 
element of the cone. Whatever 
the curve cut from the surface 
of the cone may be, the front 
view of it is the straight line, aa. 
Let Iv be the front view of any 
point 1 in the curve. IH can 
be found as in Article 89 c or 
89 d. By assuming a number 
of points in the front view of 
the curve and finding the corre- 
sponding points in the top view, 
the top view of the curve itself 




FIG. 113 




can be drawn. This top view, how- 
ever, is not the true outline of the 
section cut. This true section is 
shown to one side by a method sim- 
ilar to that of Articles 95, 96, and 
97. The true outline is a parabola. 




FIG. 114 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



75 




FIG. 115 




In the true section, what distance 
is equal to aa f 

(c) ELLIPSE. 

In figure 116 the cutting-plane 
is perpendicular to V, but the angle 
it makes with H is less than the 
angle between an element of the 




FIG. 116 




cone and the base. The front view of the curve is a straight line, aa. Assume 
points in this line, and find the top view of the curve as in the preceding article. 



The top view is not the true outline of the section ; this is, accordingly, shown 
to one side. The true outline is an ellipse. 

REMARK : The top view of the section in this particular illustration cannot be dis- 
tinguished by the eye from a circle ; it is in reality an ellipse. 

PUOBLEM : A much quicker method is to construct the ellipse on its two axes. 
How can the lengths of the minor and major axes be found ? 

CONIC SECTIONS. 

Let X represent the angle an clement of a right circular cone makes wilh the plane of 
the base. When this cone is cut by a plane, making an angle with the plane of the base : 

Greater than X, the curve cut 
from the surface of the cone is a hy- 
perbola. 

Ki/iiitl to X, the curve cut from the 
surface of the cone is a parabola. 

Less than X, the curve cut from the 
surface of the cone is an ellipse. 

99. SQUARE PRISM. Face at 
an Angle with V ; Axis Perpendic- 
ular to If. Cutting -plane at an 
Angle with H, Perpendicular to V. 

The front view of the section *K"" WlR) 

cut is a straight line, aa. Revolve 
this section about an axis perpen- 
dicular to V, through the point a, 
until it is parallel to II (Fig. 117). 
The section will then appear in the 
top view in its true outline. 

QUESTION : "When the section is re- 
volved, the front view of each limiting 
point will move in an arc of a circle as in- 
dicated in the figure until the front views 
of all these points are in a line, through FIG. 117 

a, parallel to the ground line. (Why?) 

Why do the top views of the corners of the prism all move in lines parallel to 
the ground line during revolution ? 

100. HEXAGONAL PYRAMID. 

Let Figure 118 represent any hexagonal pyramid, the axis of which is ver- 
tical. The cutting-plane is parallel to V, a distance X in front of the axis; 
The top views of the points in which this plane crosses the edges of the 




76 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWINC 





pyramid are seen from inspection to be b and b. 
The plane cuts the perimeter of the base in o and . 
The points av, bv, bv, and av are easily found and 
the true outline of the section cut determined. 

QUESTION : Why should the lines between the points 
found in the front view be straight ? 

101. REMARK : A solid is sometimes cut by a plane 
at an angle with H and with V. Such a section involves 
more descriptive geometry than it is thought wise to in- 
troduce into an elementary work of this kind. To be able 
to draw the more difficult sections and intersections, one 
needs to study descriptive geometry itself. 

INTERSECTION OF SURFACES. 

102. When any two surfaces meet each 
other, they have a definite line of intersection 
that is, a line common to both. Sometimes 
this line of intersection is a straight line, as, 
for example, when two plane surfaces meet, 
or it is a circle, as when two spherical surfaces 

intersect ; but more often it is a cm*ve, to determine which a geo- 
metrical construction is necessary. The most general problems of 
intersection are difficult of solution. In practice, however, nearly 
every object is bounded by plane faces or surfaces of revolution, the 
position of which with respect to H and V may be so assumed as to 
render the work of finding their intersection easy. 

103. General Method. A general method for finding points on 
the line of intersection of two surfaces is here given. It is assumed 
that at least one of the surfaces is a curved surface. 

Pass a plane such that it will cut at least one line from each of the 
two surfaces. The point in which a line cut from one surface meets 
a line cut from the other surface is a point on the line of intersection. 
(For since it is in each of the lines, it is in each of the surfaces.) As 
many such auxiliary parallel planes should be passed through the two 
surfaces as may be necessary to give points close enough together to 
determine the curve of intersection. 



Fra. 118 



Each auxiliary plane will usually give at least two required points more often 
four. The plane should be so chosen that the line cut from either surface is one easily 
drawn, as, for example, a straight line or a circle. Thus, for a cylinder, pass planes 
parallel or perpendicular to the axis ; for u cone, however, they should be through the 
axis or perpendicular to it. 

104. INTERSECTION OF Two CYLINDERS. 

Let the axes of two cylinders of different diameters bisect each other at 
right angles. The axis of one cylinder is perpendicular to II, the axisof the 
other parallel to both H and V. 

Conceive a plane passed through both cylinders parallel to V (Figs. 119 and 
121). This plane will cut from the surface of the horizontal cylinder two ele- 
ments, the front views of which are easily found (Art. 91). The front views of 
the two elements cut from the surface of the vertical cylinder are found as in 
Article 92. 

The points in which the elements cut from the cylinders intersect are points 
in the curve of intersection. The points indicated by the small circles in Fig- 
ure 121 are the front views of these points, and therefore lie in the front view 
of the curve of intersection. 

By passing a number of these auxiliary planes parallel to V, a series of 
points may be obtained through which the front view of the curve of intersec- 
tion may be drawn. This curve is shown in Figures 120 and 122. 

QUESTIONS : What is the top view of the curve of intersection ? 

The plane passed through the two axes of the cylinders will give the extreme out- 
side poinis of the curves. (Why ?) 

The plane passed tangent to the smaller cylinder will give the extreme inner points 
of the curves. (Why?) 

Why would it be useless to pass a plane through the larger cylinder but too far in 
front to cut the smaller cylinder? 

The invisible portion of the curve on the hack of the cylinders is directly behind 
the visible portion. (Why?) 

PROBLEMS : (1) Substitute for the vertical or the horizontal cylinder a cylinder 
with its axis parallel to V but at angle (say of 45) will) H. 

(2) Assume the axes of the two cylinders parallel to H. 

(3) Let the axis of the smaller cylinder be a short distance in front of or behind the 
axis of the larger cylinder. 

For these three problems use the method explained above. In (2), however, the 
auxiliary planes are passed parallel to II, and in (3) pass planes back of the axis nearot 
V to find the invisible portion of the curve of intersection. 

REMARK: Let a triangular prism, square prism, hexagonal prism, or other similar S( 'lid 
be substituted for the vertical or horizontal cylinder. Planes parallel to V cut straight 
lines from the cylinder and the solid, and the points of intersection are found as before. 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



77 





FIG. 119 



FIG. 120 




FIG. 121 



FIG. 122 



78 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 




FIG. 123 



FIG. 124 







105. INTERSECTION OF CYLINDER 
AND SPHERE. 

In Figures 123 and 124 the axis of 
the cylinder is vertical, but does not go 
through the centre of the sphere. The 
auxiliary plane in this case is passed 
parallel to V. The two elements cut 
from the cylinder meet the circle cut 
from the sphere ( Art. 93 ) in four 
points. These four points for each 
auxiliary plane are found in the front 
view, and the curve of intersection is 
thus determined. 

In this intersection the invisible portion 
of the curve is not directly behind or be- 
low the visible portion. Auxiliary planes 
passed back of the axis of the cylinder or 
centre of the sphere will give points on the 
invisible portion. (Why ?) 

QUESTIONS: Assume the axis of the cyl- 
inder to puss through the centre of the sphere. 
What is the curve of intersection ? 

What auxiliary plane will give the low- 
est point of the upper curve of intersection 
and the highest point of the lower curve? 

What auxiliary plane gives the extreme 
right and left points of the curve of inter- 
section ? 

PROBLEM : Assume the cylinder with its 
axis to the right or left of the centre of the 
sphere, and a rniall portion of the cylinder 
not passing through the sphere at all. Use 
the same method. 



Fio. 125 



FIG. 126 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



79 



106. INTERSECTION or CYLINDER 
AND CONE. 

Assume the axes of a cylinder and 
a cone to intersect at right angles, the 
axis of the cylinder parallel to II and 
V (Figs. 127 and 128). A horizontal 
auxiliary plane will cut straight lines 
from the cylinder and a circle from the 
cone (Fig. 129). The two elements 
cross the circumference of the circle in 
four points, the top and front views of 
which are shown in Figure 129. Thus 
a number of auxiliary cutting-planes par- 
allel to H will determine the top and 
front views of the curve of intersection. 

NOTE : In this problem the top views 
of the points of intersection are first found, 
and from them the front views are deter- 
mined. 

QUESTIONS : What auxiliary plane gives 
tlie highest point in the front view of the 
curve ? Lowest 1 

What point of each curve is given by a 
plane through the axis of the cylinder? 

Why not pass auxiliary planes parallel 
to V ? 

Why is the invisible portion of the curve 
directly behind the visible portion (front 
view)? 

PROBLEMS : (1) Assume the axis of the 
cylinder in front of the axis of the cone. 

(2) Assume the cylinder high enough up 
to cut the cone in two. 

Use the method explained above for both 
problems. 




Fm. 129 



FIG. 130 



80 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



107. INTERSECTION OF CYLINDER AND HEXAGONAL PRISM. 

Let the axes bisect each other at right angles ; axis of the cylinder vertical. 
The method is the same as for two cylinders (Art. 104). The work is indicated 
in Figure 131. 

108. INTERSECTION OF HEXAGONAL PRISM AND SPHERE. 

Use the method of Article 105. The work is indicated in Figure 132. 




Fir,. 131 



FIG. 132 



109. DEVELOPMENT OF SURFACES. When a surface is unfolded or 
unrolled into a plane, the outline is called its development. Only 
cylinders, cones, and plane surfaces can be thus developed. 

The surface may be opened or cut at any desired point to begin the development. 

110. (a) Development of the Smaller Cylinder of Figure 122. In 
Figure 122 let it be required to develop one end of the smaller cylinder, 
and for sake of clearness in explanation let this end be taken by itself 
(Fig. 133). When unrolled, the circumference of the base will become a 




FIG. 133 

straight line, aa, the length of which is computed from the diameter of the 
cylinder. The distance from the base to the curve of intersection can be 
measured at regular intervals and transferred to the development as follows: 
(1) Draw any number of elements equal distances apart on the surface of 
the cylinder. This is done by revolving the circumference to the position 
indicated by the broken circle, dividing it and revolving it back again. Draw 
the elements 1, 2, and 3. These elements are equal distances apart on the 
surface of the cylinder, although the lines themselves' are not equal dis- 
tances apart in the drawing. (Why?) (2) Divide the line aa in the develop- 
ment into as many equal parts as were laid off on the circumference. From 
each of the points thus obtained lay off the lengths of the corresponding ele- 
ments, 1, 2, 3, etc. Through the ends of the elements draw the curve. The 
surface thus obtained, if rolled together, would form a small cylinder which 
would fit against the larger cylinder of Figures 120 and 122. 

Since the curve of intersection is symmetrical, a number of the elements are of the 
same length ; these have the same numbers in the figure. Thus there are four elements 
of the same length marked 2. The development is usually found directly from the orig- 
inal view of the interseciion. 

(b) Development of the Cylinder of Figure 126. In Figure 126 an end of 
the cylinder can be developed by the method already given. Each element 
must be measured by itself, however, and the distances to the invisible as well 
as to the visible portions of the curve must be used. 

NOTE : The invisible portion of the curve is not shown in Figure 126. 

(<) Development of the Cone of Figure 130. In Figure 130 the develop- 
ment of the cylinder can be found by the usual method. In the develop- 
ment of the cone (Fig. 134) the radius of the circular arc aa is equal in 
length to an element of the cone (Why ?), and the length of the arc itself is 
equal to the length of the circumference of the base. This arc is divided 
into as many equal parts as were laid off on the circumference of the base 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



81 




FIG. 134 

of the cone, and the corresponding elements drawn from the vertex. The 
true distances along any one of these elements to points on the carve can be 
found by revolving the element until it is parallel to H or V (Art. 73), and these 
distances laid off on the corresponding element in the development. For ex- 
ample, revolve the element through the point ft (Fig. 130) until it is parallel to V. 
The point b will move to ft', and the distance from the vertex to b' will be the dis- 
tance to lay off along the corresponding element in the development (Fig. I:i4). 

111. The developments of the surfaces of Articles 90 to 100 are 
easily found by the methods of Articles 110 (a), (b), and (c). 

In finding the intersection of the surfaces of t\vo solids, it makes 
but little difference whether the axes of the solids intersect or not. 
If, however, the axes are not at right angles to each other, the problem 
is usually more difficult. (See Art. 101.) 

SHADOWS 

112. It is sometimes required to find the shadow cast bv an object on 
a horizontal or vertical plane. In this case it is best to use the first angle 
of projection, letting II and Vrepresent the planes upon which the shad- 
ow falls. If the object is in the third angle there can be no shadow 
on 11, unless light comes from below the object instead of from above it. 

REMARK The subject of shadows is of little practical value. It, however, affords 
practice in the use of the first angle of projection and furnishes examples in tinting; 
otherwise ils importance would hardly warrant the space required for explanation of 
principles. 
B 



113. Problems in shadows fall into three classes: 

F'n'xt. The shadow cast by an object on the planes of projection. 
Xii-and. The shadow cast by it upon some neighboring object. 
Third. The line of separation of light and shade on the object 
itself. 

114. SHADOWS ON H AND V. General Method. (1) Select from 
inspection of its views those limiting points of an object which cast 
shadows. 

A point of an object casts a shadow when the ray of light which strikes it, if pro- 
duced, meets H or V irif/mn/ /xnwinf/ through any part of the object. 

(2) Find where the ray of light through each of these points pierces 
II or V. 

The direction of the rays of light is assumed to be such that each of the two views 
of any particular ray makes an angle of 45 with the ground line. 

(3) Draw the outline of the shadow through the views of the 
points found in 2. 

115. To FIND WHERE ANY LINE PIERCES H OR V. To find where 
the line 1-2 (Fig. 135) pierces II, produce its front view, Iv 2v, until 
it meets the ground line in 

Xv. The two points, Xv and 
XH, are the two views of the 
point in which the line 1-2 
pierces H. (Why?) If the line 
meets V instead of H, the 
views of the point are found 
as indicated in the figure for 
the line 3-4. 

Every ray of light, if produced, 
must meet both planes of projection, 
since the latter are of indefinite extent. 
Thus, in Figure 135, the ray 1-2 meets 
the horizontal plane at XH and the ver- 
tical plane at Yv. 

Shadows are never drawn behind 
or below the ground line, but it is some- 
times necessary to find out where a ray 
would go if produced. FIG. 135 




! X 


y ! 


! /"XH 
/4H 




UNIVERSITY 



82 



AN INTRODUCTORY COURSE IX MKrilAXK'AI. ])H.\\VIX<; 




FIG. 1 36 



I -4V 2-3 V 




IH 



116. SHADOW OF 
A SQUARE PRISM ON 
II. 

If the base of the 
prism (Fig. 136) is in 
II, the points 2, 3, and 
4 cast shadows. A 
ray of light through 1, 
for example, must pass 
through the prism to 
reach H ; therefore 1 
does not cast a shadow. 
The points in which the 
rays of light through 2, 
3, and 4 pierce H are 
respectively X, Y, and 
Z. The views of these 
points are found, and 
the outline of the shad- 
ow drawn as indicated 
in Figure 137. 



117. It is evident from the above example that : 
(1) //' n n edge of an object is parallel to a plane, its shadow mi tit at 
plane is a line parallel to itself and of the same lerujtlt. If an >/ plane 
surface is parallel to a plane, the shadow on that plane 'in identical in out- 
line with tin' xiufairlfx, If. 

.^^^^ (2) Vertical <-</</ix in 

an object <-ast, Jfi> lines in 
the shadow. 

When a surface is parallel 
to a plane it is usually neces- 
sary simply to fititf the shallow 
cast by one of its limiting points 
to determine the whole shadow. 

118. SHADOW ON H 

AND V. 

If an object is too near V, 
part of the shadow will fall 
on V. Figures 138 and 139 
Km 138 







Kin. 139 



KIG. 140 



Sl'ICCIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION 



83 




FIG. 141 




Kio. 142 



illustrate such a case, the prism 
of Figure 130 having been moved 
nearer to V. In this example, it 
is iiDcessary to find where certain 
rays of light pierce V instead of 
H (Art. 115). The method is 
indicated for the ray of light 
through one corner by dotted 
lines (Fig. 139). 

119. SHADOW OF A HEXAG- 
ONAL PRISM ON II. 

The method used is exactly 
like that of Article 110. The 
work is indicated in Figure 140. 

120. SHADOW OF A CYLIN- 
DER ox II. 

Figures 141 and 142 illus- 
trate the shadow of a cylinder 
with its axis vertical. Since the 
upper base is parallel to H, its 
shadow is a circle. Hence find 
the point in the shadow where 
a ray of light through the centre 
of the upper base would strike 
H. The whole outline is then 
easily found. 

121. SHADOW OF Two 
BLOCKS ON H. 

Figures 143 and 144 illus- 
trate the shadow of two blocks 
on H. Note that points in the 
lower base of the upper block 
cast shadows. 

122. SHADOW OF CIRCLE 
PARALLEL TO V. 

Figure 145 shows the top and 
front views of a circle parallel 




Fio. 143 





FIG. 144 

to V. Its shadow on II is an ellipse, points of which are easily found as 
illustrated by Is. 



84 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



123. SHADOW OF CIRCLE PERPENDICULAR TO II AND V. 

Figure 146 is another common case where the circle lies in a profile plane. 
The shadow construction is different from the preceding problem, because one 
view of a point on the circumference cannot be determined by dropping a per- 
pendicular from the other view. Let any point, as Iv, be given; In can be 
found as indicated. Draw rays through these points and proceed as before. 



IV 










IS 



IH 



FIG. 146 



foregoing 
Amuch 



134. SHADOW OF ONE OBJECT UPON ANOTHER. The 
paragraphs relate to shadows on the co-ordinate planes only, 
more difficult problem is to find the shadow cast upon some second 
body whose shape is known. The general method is to draw the 
views of the rays thropgh limiting points of the object which cast 
shadows, and find where these rays meet the surface which receives 
the shadows. The difficulty lies in finding out where the rays meet the 
surface in question. A different method has to be employed in each 
case, depending upon the surface on which the shadow falls. 

125. SHADOW OF A PART OF AN OBJECT ON ANOTHER PART. 




FIG. 147 



Figure 147 is an example where the 
shadow upon the object itself has to be 
determined as well as the shadow on the 
horizontal plane. 

The object is a square prism with a 
square projecting rim, and its shadow 
on the horizontal plane is found by tlie 
method already explained. 

The method of finding the shadow 
of the rim on the lower part of the prism 
is indicated for one point by the dotted 
lines. Thus in the top view, for exam- 
ple, the dotted line through the front 
corner represents the top view of a ray 
of light through the under corner of 
the rim. This line is drawn until it 
strikes the front face of the prism. 

The point on the front face thus found is a point in the shadow and is pro- 
jected up to the front view. 

The dotted line through the upper left-hand corner (front view) is drawn 
until it strikes the rim, and the top view of the point thus found is a point of 
the shadow cast by the prism on the rim. 

126. SHADOW OF A CONE UPON A CYLINDER. 

In Figure 149 the direction of the light was assumed in such a way as to make 
the shadow correspond to that in the photograph (Fig. 148). The dotted lines 
through the vertex of the cone (front view) and the shadow of the vertex (top view) 
indicate the directions of the front and top views respectively of a ray of light. 

The shadows of the cylinder and cone on the horizontal plane can be found 
separately by methods already described (using, however, the new directions for 
the views of a ray of light). Shadows of the cylinder ends are found as in 
Article 122. 

To find the shadow of the cone on the cylinder, first find the two elements 
of the cone which determine the shadow. To do this, imagine a horizontal 
plane through the base of the cone and find the point where a ray of light 
through the vertex would pierce this plane. (The/roni view of this point is at 
6.) From the top view of this point (not shown in the figure) draw tangents 
to the top view of the base of the cone, and from the points of tangency draw 



SPECIAL APPLICATIONS OF ORTHOGRAPHIC PROJECTION* 



85 




FIG. 148 





lines to the top view of the vertex. These two lines will be the top views of 
the required elements. The front views of these elements are easily found ; 
they are lines from the vertex to Iv and 1'v. 

On the front view of one of these elements assume a point as a, and find a 
in the top view. Through a in the front view draw the front view of a ray of 
light until it strikes the circle (front view of the cylinder). The point of con- 
tact is the front view of the point in which this particular ray of light strikes 
the surface of the cylinder. The corresponding top view is easily found, and is 
in the edge of the shadow. By assuming a number of such points and repeat- 
ing the process, the outline of the shadow can be determined. 

REMARKS : The dotted circle (top view) is used simply to find the top views of a 
and a', points assumed for illustration in the front view. 

The element from the vertex to Iv in the front view appears like n vertical line. 
It is not quite vertical. If the rays of light had been assumed in the usual way, this 
element would have \>cen in the left-hand portion of the cone. 

The curved edges of the shadow are portions of two ellipses. The ellipses corre- 
spond to those which would be cut from the surface of the cylinder by two planes. 
Through what lines would these planes be passed ? 

If a line is drawn from the centre of the circle (front view of the cylinder) perpen- 
dicular to the front view of a ray of light, it will cut the circumference in a point which 
is a front view of an element. The top view of this element terminates the shadow c,f 
the cone on the cylinder. 

A portion of the base of the cone casts u shadow on the cylinder. If this were not 
so, the curve forming the edge of the shadow would not reverse. This portion of the 
shadow is found by assuming points in the circumference of the base (instead of iu 
cither of the two elements) and proceeding as before. 

127. The line of separation of light and shade on an object can usually be deter- 
mined by inspection after the shadows on the co-ordinate planes have been found. In 
many cases it can be determined by preliminary inspection without drawing a line. 
When the body has projecting edges which cast shadows on itself, the problem is like 
that of Article 126, and may become quite difficult, 

128. SHADE LINES. (See Art. 36.) The shadows described in the 
preceding paragraphs are rarely constructed except on important 
drawings which are finished up with a brush. Ordinarily, no brush- 
shading is used, and the appearance of the drawing is much improved 
by the use of shade lines (Art. 3fi). 

It is almost universal, in working drawings, to shade the right- 
hand and lower edges in all views. This is equivalent to changing 
the direction of the ray of light in top views and end views. 



FIG. 149 



86 



AN INTRODUCTORY COURSE IN MECHANICAL DKA \\I\i; 



Adhering to the common method, these general rules may be 
given : 

(1) Shade right-hand and lower edges in all views. 

(2) Shade left-hand and upper edges of all holes. 

(3) Lines between visible planes are not shaded. 





FIG. 150 



FIG. 151 



The lower right-hand quadrant of outer circles and the upper left-hand quadrants 
of inner circles are shaded (Art. 36 b). 

NOTE: In some of the line drawings illustrating shadows the above method was 
not used. The draftsman needs to use judgment, and common -sense iu applying 
general rules, remembering that a shade line should lie between a light and a dark 
surface. 

129. It should be noted that curved surfaces, like cylinders and 
cones, have no abrupt line of demarcation between light and shade. 
The lightest portion'of such surfaces is that normal to the rays of 
light, and the darkest is tangent to the rays; the depth of shade de- 
pends on the amount of light reflected from each part. The shading 
should be lightened somewhat at the very outside edge of curved 
surfaces to give the appearance of light reflected from adjoining 
objects. 



CHAPTER VII 



I' K KS ] KCT I V E 



Bv K H. LOCKWOOD, M.E. 



130. INTRODUCTORY. Except- in architecture, but little application 
of perspective is made in Mechanical Drawing. The conventional 
isometric and cabinet projections which are used as a substitute are 
easier to execute from measurement, but they do not always give a 
satisfactory appearance. The principles of perspective, however, are 
not difficult to acquire, and they can be applied in a' mechanical way 
without special artistic training; nevertheless, distorted results may 
follow, even from a correct application of the laws of perspective, if 
they are applied to absurd or limiting positions. For example, to 
represent on paper the appearance of a six-inch cube at a distance of 
th !>< inches from the eye is an absurdity, yet it can be drawn by the 
rules of perspective as easily as in any other position. It should be 
remembered that a perspective drawing represents the object as it 
actually appears to the eye ; hence the best point of view should be 
obtained, and good judgment in this matter is as important as a formal 
knowledge of the rules of perspective. 

131. PERSPECTIVE DRAWING DEFINED. As treated in mechanical 
drawing, the problem of perspective is : Given the top and front views 
in orthographic projection (Chap. V.), to construct the perspective 
projection. 

The subject is sometimes called linear pertptctfaf, since it relates only to the lines 
of the drawing. Perspective is evidently more laborious than orthographic projection, 
because the top and front views, instead of being the end sought, are only preliminary 
to it. But the top and front views need not be drawn complete in all cases. Some- 
times they may be drawn only in part, or omitted altogether. 

The relation of perspective to orthographic projection must be 
kept clearly in mind from the start. In Figure 152 the object is in 



(Eye) 




Fin. 152 

the third angle, the top and front views being drawn in the usual way. 
The eye is in the fourth angle, in order to see the object through the 
vertical plane, which is assumed transparent. The perspective draw- 
ing is made on the vertical plane, the outline being determined by 
straight lines drawn from the object to the eye. The intersection of 
these lines (or rays) with the vertical plane gives a drawing which, if 
shaded and colored, would exactly represent the object as seen from 
the assumed point. 

In most treatises on Perspective the object and the eye of the ol>server are taken in 
the first angle. Then it is not convenient to make the perspective drawing on V. An- 
other plane is assumed parallel to V, and placed between the object and the eye, and is 
called the Picture Plum , 



88 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



The term Picture Plane will be employed in this chapter, though it is coincident in 
every case with V. 

132. PICTURE PLANE. The plane on which the perspective draw- 
ing is made is called the Picture Plane. 

The plane of the paper, therefore, corresponds to the picture plane. In this chap- 
ter the picture plane coincides with V, the vertical plane of projection, in every case. 

133. POINT OF SIGHT. The position of the eye is called the Point 
of Sight (Fig. 152). It is denoted by the letter S (projections Sv, SH). 
"Where no ambiguity would result, the vertical projection of the point 
of sight is also denoted by S. 

The perspective drawing varies with every position of the eye, even if the object is 
fixed, as is evident from Figure 152. Hence the importance of choosing the best position 
for the point of sight. This is immaterial for the present, however, since the methods 
are the same wherever the point of sight is chosen. 

134. ELEMENTARY CONSTRUCTION. The simplest construction of a 
perspective drawing is based upon the use of two projections of the 




'-- M 



5V 




3-4v 



FIG. 153 



point of sight. The method is illustrated in Figure 153. Sv and SH 
are the two projections of the point of sight in the fourth angle (Art. 
131). In the fourth angle a point is below and in front of the ground line. Hence 
its two views are on the same side of the ground line. The pyramid 1 2 .3 4 5 
is given in the usual way by the top and front views. 

(a) Join In, 2n, etc., to SH. These lines are the horizontal pro- 
jections of rays to the point of sight, and need be drawn only to GL. 

(1) Join l-2v, 3-4v, 5v to Sv. These lines are the vertical pro- 
jections of rays to the point of sight. 

(c) From the intersection of each line of the first group (n) with 
GL, drop perpendiculars to the corresponding line of the second group 
(J). The outline IP 2p 3i>, etc., thus determined, is the perspective of 
the pyramid. 

It will be seen that making a perspective drawing by this method is a simple proc- 
ess. Its defect is the use of SH, which generally falls beyond the limits of the drawing- 
board. Hence, in actual work, a modification of this method, not involving SH, is used. 
This construction is of fundamental importance, however, and should be understood 
before using the abridged method. 

135. LINES IN SPECIAL POSITIONS. The perspective of any line 
can always be determined by the method of Article 134. Yet in some 
cases the perspective can be found much more simply, at least as far as 
its direction is concerned. There are three important cases '. 

(a) When a line is perpendicular to the picture plane, if.* j r^j >////',-,> 
Converges towards Sv. See Figure 153 for an example, where the line ln-2a is 
perpendicular to the picture plane (V) and its perspective li>-2p points towards Sv. 

(b) W/ten a line is parallel to the picture plane, its perspective is 
parallel to the front view of the line. See Figure 153, where the line lH-4n 
is parallel to the picture plane and the perspective lp-4p is parallel to l-2v 3-4v. 

(c) Horizontal lines at 4-5 to the picture plane converge 'in perspec- 
tive towards points on either side of Sv, and at a distance from Sv equal 
to that of the 2^0 hit ftf sight from the picture plane. 

The truth of the above statement can be demonstrated from Figure 154. lv-2v and 
lH-2n are the front and top views of a horizontal 45 line, one end of \vhicb is in the 
picture plane. The perspective of the line is lv-2p, found by the method of Article 134. 
Now, instead of terminating the line at 2. let 2 recede indefinitely to the right along the 
line. The dotted line joining Sv to 2v will become a horizontal line through Sv. The 



PERSPECTIVE 



89 



G b 




/ 
^- L 



Sv 

n." 



-v^D 



, IV 2V 



""SH 



FIG. 154 



line joining Sri to 2n will become a 45 line through SH crossing GL at a. Dropping 
a perpendicular from a, the perspective of the point (when infinitely distant) is found 
at D. Hence the perspective of the line 1-3 extends only from Iv to D, however long 
the line itself rany be. But Sn-b (=Sv-D) is the distance from the point of sight to 
the picture plane (Fig. 152) ; hence the statement is proved. 

Since the location of D depends only on the direction of 1-2, and not on its posi- 
tion, it follows that any line parallel to 1-2 would also converge towards D. 

Horizontal 45 lines sloping in the opposite direction would converge towards a 
point situated at an equal distance to the left of Sv. 

136. HORIZON. A horizontal line through the vertical projection 
of the point of sight is called the horizon. It is used for construction pur- 
poses only, and contains the important points D on either side of Sv (Art. 135 e). 

137. POINTS OF DISTANCE. Points in the horizon at a distance 
from Sv equal to that from the point of sight to the picture plane are 



called the Points of Distance, or Measuring Points. They are denoted 
by the letter D. 

The distance from the eye (point of sight) to the paper (picture plane) is the first 
thing to be assumed in making a perspective drawing. Hence the location of the 
points D, D, is always known. Horizontal 4o lines always extend, in perspective, tow- 
ards one of these points (Art. 135 cj. This gives a method of measuring distances along 
lines perpendicular to the picture plane (Art. 135 a); hence the term measuring points. 

138. VANISHING POINTS. In perspective, parallel lines converge 
towards a point called the Vanishing Point. Every set of parallel 
lines has its own vanishing point, depending on the direction of the 
lines. All horizontal lines vanish somewhere in the horizon. If per- 
pendicular to the picture plane they vanish at Sv (Art. 135 a). If 
horizontal 45 lines they vanish at D (Art. 135 c). 

139. CONSTRUCTION OF THE DRAWING. -By using the measuring 
points (Art. 137) the horizontal projection of the point of sight may 
be omitted. This overcomes the defect of the method described in 
Article 134. The vertical projection of the point of sight will here- 
after be denoted by S. 




3-4-V 



90 



AN INTRODUCTORY COl'RSK IN MECHANICAL DRAWING 



In Figure 155 the projections of the pyramid In, Iv, 2n, '2v, etc., are 
taken exactly as in Figure 153, Article 134, in order that the two meth- 
ods may be compared. The following are the steps of the process : 

(a) Assume S at any desired point and draw the horizon through it. 

(b) Take D at any arbitrary distance on either side of S. 
Hints regarding the choice of these two points will be given later (Art. 144). 

(c) Connect each corner of the vertical projection to S by dotted 
lines (Art. 135 a). 

(d) Draw a horizontal line through l-2v, and lay off on it to the 
left distances equal to a-lu, a-'2n from the top view, giving b and c. 

(e) Join b and c to D, and get the desired perspective of the two 
points at IP and 2p. 

(/) The pyramid can be completed from these points, because 
IP^IP is parallel to (i^2v)-(3-4v) (Art. 135 5), and likewise 2p-3p. 
Draw diagonals of the base and erect a perpendicular to get the 
vertex, or find it by measurement as shown by the dotted lines. 

The truth of the method employed to find IP and 2p rests upon 
the fact that the lines joining b and c to D are 45 lines (Art. 135 c). 
Hence right triangles are formed with the right angle at lv-2v. The 
opposite sides are equal, as (l-2v)-ft=lH-a. Therefore the correct 
measurement is made from lv-2v towards S. 



PERSPECTIVE. 



140. REDUCED POINTS OF DISTANCE. The eye is generally assumed 
at such a distance from the paper that D falls beyond the limits of 
the drawing-board. This difficult} 7 is easily avoided by using reduced 
points of distance that is, new points at one- half, one-quarter, or 
some other simple fraction of the distance from S to D. The con- 
struction is shown in Figure 156. D is inaccessible, and it is desired 
to measure 2" from Iv towards the point of sight. Take D/ 2 half-way 
out to D, lay off 1" to the left of Iv, and join. The point IP thus ob- 
tained is the same as if the full size dimensions were used. If 
D/4 had been used, one quarter of 2", i. e., |" would have been 
measured to the left of IV ; if Din, one eighth of 2", and so on. 



I Q PERSPECTIVE. 

i -** 141. ANOTHER EXAMPLE. 

When none of the lines of the 
l figure are parallel or perpendic- 

j^ ular to the picture plane, more 

construction lines are needed, but 
I 1 " the process is the same. Figure 

157 shows a pyramid with its axis 
vertical and one edge of the base 
inclined to the picture plane. 

The top and front views, ground line, horizon, S and D, are assumed 
in advance. Eeduced points of distance are used. Each point of the 
front view is joined to S by dotted lines, and the points are located in 
perspective as shown in the last article. The only point needing ex- 
planation is the vertex. 5v is so near the horizon that it is best to 
project it to the ground line, perform the construction there for deter- 



FIG. 156 




4P 



2v Iv 3v 4v 
FIG. 157 



PERSPECTIVE 



91 



mining the perspective, and project down to or. The vanishing points 
of the opposite sides of the base are at V and V in the horizon. Only 
V is shown in Figure 157, as the other point falls beyond the limits of 
the figure. 

142. CIRCLES IN PERSPECTIVE. All circles will appear as ellipses 
unless their plane is parallel to the picture plane. The best method 
of drawing them is to construct a circumscribing square and sketch 
the ellipse freehand through eight points, which can be easily deter- 
mined. Figure 158 shows a cube with one face in the picture plane 
and a circle inscribed in each face. The eight points through which 
each ellipse passes are evident by inspection. 





FIG. 158 

Figure 159 shows the same cube with inscribed circles when no 
face is parallel to the picture plane. No explanation is needed, as the 
construction is evident from the figure. It is possible to obtain the 
major and minor axes of the ellipse, but for practical work it is not 
necessary. 

A good example of a circle which appears as an ellipse in true perspective is 
furnished by Fig. 103, page 72. 

143., SPACING EQUAL DISTANCES. The following is a useful method 
of spacing equal distances in perspective. Figure 160 shows the 
method applied to a line converging towards S. Lines 1 and 2 are 




FIG. 159 

given, and it is required to draw others, parallel and equidistant. 
Join 2 to any convenient point, V in the horizon, and produce to 1'. 
1-1' is a horizontal line. Draw a line from 1' to S, which gives 2' on 
a horizontal through 2. Join 2' to V and get 3. Eepeat the operation, 
and any desired number of points can be obtained. 

The ordinary way of measuring would be cumbersome in this case, 
if many equal divisions were required. 

144. CHOOSING THE POINT OF SIGHT AND v_ 
POINTS OF DISTANCE. -While the choice of \'-v 
these points is entirely arbitrary, some gen- \ 

eral directions may be given. It should be 
remembered that the distance from S to D is i 
the actual distance from the eye to the pict- 
ure plane. This depends on the size of the U''____l!/' 
paper, and is frequently made about twice the FIR. ieo 



S 

T 



92 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



diagonal of the sheet. If the distance is made too small, the result 
is a picture having " steep perspective." 

A single large object, a house for example, should be viewed from 
a distance equal to at least twice its greatest dimension. If, for ex- 
ample, the height were 40 feet, the point of view might well be 80 
feet away. Then the plan and elevation drawn to a scale of -i feet to 
the inch would make S to D equal to 20 inches, and produce a per- 
spective drawing something less than 10 inches high. 

It is generally best to place the point of sight nearly in front of a 
large object, as a building, in order to get the most natural appear- 
ance. The plan must then be inclined to the picture plane. An easier 
but less satisfactory way is to place one face of the object in the pict- 
ure plane and station the eye to one side. This is shown, for a skele- 
ton house in Figure 161. 

Figure 162 shows the more approved arrangement. A sufficient 
number of dotted lines are given to explain the principal constructions. 




FIG. 161 



FIG. 162 



CHAPTER VIII 



WORKING DRAWINGS 



145. A drawing is a working drawing when it gives all the infor- 
mation necessary to make the object it represents. A working draw- 
ing may be divided into three parts: 

(1) The outline drawing showing the shape of the object. 

(2) The dimensions giving the size of every part. 

(3) The lettering i. e., printed explanations and directions. 

A working drawing should be so complete that one can make the object from it 
without asking questions. It is evident, then, that dimensions and printed notes are 
essential purls of such a drawing. 

If working drawings are made according to some common method 
understood and agreed upon by those who use them, the advantage to 
all concerned is obvious. Hence the development from the crude free- 
hand sketch to the modern shop or working drawing. 

While the method of making a working drawing varies somewhat in its minor de- 
tails, the general method is everywhere the same. Hence there are certain definite rules 
by which the draftsman must be governed if he wishes his drawing to conform to the 
standard practice. The most important of these rules can be observed by the student 
at the outset. A manufacturing company often requires its draftsmen to observe cer- 
tain customs adapted to its own work ; these simply supplement the rules above re- 
ferred to. 

146. In making a working drawing the aim should be : 

(1) To make it conform to the standard practice. 

(2) To show the shape and give the size of every part of the object. 

(3) To answer in advance all reasonable questions one might ask 
in making the object. 

(4) To work quickly without sacrificing accuracy or neatness. 

147. In working drawings the object is represented by two or 
more views, eacli of which is drawn according to the principles of or- 



thographic projection (Chaps. V. and VI.). Hence these views are 
really projections, not pictures (Art. 62 c). As many such views are 
shown as may be necessary to completely represent the object (Art. 
62). The arrangement of views depends on which angle of projection 
is used (Arts. 61 c and 64 V). In the third angle the top view is drawn 
above the front view, the bottom view below the front view, the end 
view nearest the end it represents, and so on. In the first angle the 
positions of the views are reversed the top view is below the front 
view, the bottom view above it, and so on. Since both methods of ar- 
rangement are used, it is well to mark each view, as, for example, END 
VIEW T , TOP VIEW, etc. 

REMARK: Experienced draftsmen seldom think of the planes of projection at all 
(Art. 64: d). 

Ground lines arc usually omitted, and the distance of the object from II or V re- 
spectively is immaterial. 

When a section view is drawn the point at which the section is 
taken is indicated on one of the other views. The usual way is to 
draw the trace of the cutting-plane, lettering it, and marking the sec- 
tion view to correspond, as, for example, SECTION AT AA. (See section 
view, Plate 1, page 101.) 

The portion of the object behind the cutting-plane is shown in 
the section view when it helps to explain the section, otherwise it is 
omitted. 

"When an object is symmetrical with respect to an axis, and a sec- 
tion view is needed, it is often sufficient to show a half section com- 
bined with a half of another view. Thus, in Figure 163, a half end and 
a half section view is shown. 



94 



AX INTRODUCTORY COURSE IN MECHANICAL DRAWING 



For the location of a section view no rigid rule can be followed; 
the draftsman is often obliged to place it in some particular space by 
the arrangement of the other views. If possible the following ar- 
rangement should be observed when the portion of the object back of 
the cutting-plane is shown : A section seen from above occupies the 
same position as a top view ; looking from the right towards the left 
the same position as a right-hand end or side view ; from below 
the same position as a bottom view, and so on. When the section 
view shows only the portion of the object cut, its location is of little 
importance, but, in general, it should be as near as possible to the view 
which shows where the section is taken. 

148. THE DRAWING To SHOW THE SHAPE. The drawing shows 

the shape of the object. It may be made to any convenient scale, as 

full size, half size, quarter size, and so on. In drawings of large objects 

scales of " = I'-O", or 1" = l'-0", or If = I'-O", or 3" = 1'-0" are com- 

: monly used. In this case measurements on the drawing are best laid 

; off by means of the " Architects' Open Divided Scale." (See Art. 21.) 

Shop units are feet and inches, and halves, quarters, eighths, six- 
teenths, and thirty-seconds of an inch ; the decimal scale is, therefore, 
not often used in working drawings. 

Drawings are first made in pencil. If a number of copies are re- 
quired, instead of inking the drawing on the original sheet a tracing 
is made (Art. 43) and blue prints taken (Art. 42). Experienced drafts- 
men often make the drawing directly on the tracing-linen itself. The 
size of the sheet depends upon the nature of the drawing. Sheets 
36" x 24" and under are preferable to those of larger size if the limits 
of the drawing will permit. If several different sheets of drawings of 
the same object are needed, it is well to make them all of one size. 

A drawing which represents the object as it will appear when fin- 
ished, with each part in its proper place, is called an " assembled draw- 
ing." A " detail drawing " shows each part by itself. In the latter 
case parts adjacent in the object should, in general, be near each other 
in the drawing. Small details are sometimes shown by themselves 
to larger scale if clearness is gained thereby. Parts made on the same 
machine or by similar processes are often collected on separate sheets. 



(Thus there may be sheets of bolts, screws, forgings, castings, etc.) 
This is only done where large numbers of pieces are wanted and their 
manufacture has been somewhat systematized. 

"When an object is symmetrical it is often sufficient to show one- 
half of it. Long pieces can frequently be " broken " to save space and 
still show all that is necessary if the true dimensions are given. (See 
blade of T-square, Fig. 163.) When two pieces differ only in being 
rights and lefts, it is usually necessary to draw but one of them, noting 
on the drawing that two are wanted one right and one left. 

REMARK: Two pieces are right and left in the same sense that the two hands are 
right and left. When placed side by side they are symmetrical with respect to an im- 
aginary straight line between them, but when placed one on top of the other they do 
not coincide. It usually makes no difference irliich is called a right simply designate 
one the right, the other the left. 

Invisible lines are usually shown, unless the clearness of the draw- 
ing is sacrificed thereby. For example, if the top and bottom views of 
an object are both shown, details on the bottom, which would lead to 
confusion if shown in the top view, are omitted altogether in the top 
view, but are shown in the bottom view, where they appear as full lines. 

Open bolt and rivet holes are usually blackened, or if large thev 
are cross-lined ("hatched"). Shade-lines may be drawn as explained 
in Article 128. Some draftsmen omit them altogether. Cylindrical 
surfaces may be shaded, according to Article 37. Sometimes, in the 
drawing of one part of an object, a second part connecting with it 
and not otherwise shown is indicated by broken lines throughout to 
show better the connection. 

149. DIMENSIONS SIZE OF AN OBJECT. The size of every part of 
an object is given by the dimension figures and lines. Dimension 
lines show exactly from what point to what point the measurement 
is to be made. (See Fig. 163.) Such lines should be distinguished 
from the regular lines of the drawing. They are usually drawn in 
one of three ways: d) Fine broken lines (Fig. 163). (2) Very fine 
black lines. (3) Red lines. Red lines of tracings print more faintly 
on blue process paper than do the black lines, and this has the effect 
of making the drawing itself stand out with the dimension lines in 



WOKKIM; IKA\YIN<;S 



95 



the background. Dimension figures and the arrow heads at the ends 
id' a dimension line, however, should alwai/* > l>l<i<-k. 
t Figures should be plain, heavy, and unmistakable wont* run t>< 
,fii,xn,,l ,it, lint not ti/jni', x. It is better to leave a space in the middle 
of each dimension line for the dimension, than to write the figures 
above or below the line. If a dimension line is so short that a di- 
mension cannot be given on it, the latter is placed to one side and an 
arrow indicates where it belongs. Tin: iliim-axiim* <<// <> <li-tin'iij tiff 



Feet and inches are indicated thus, 6'-3". It is better to give 
anything twelve inches and over in feet and inches. Custom varies 
in this respect. Widths of boards, iron plates, etc., are given in 
incites when writing down the three dimensions, as, for example, 
14"x V' xlO'-O". In such a case the order of dimensions is 
width x thickness x length. The width being given first, and assumed 
at right angle to the "grain," the direction of the latter is thus de- 
termined. Thus, in a 14"x|"x8" piece, the grain is parallel to the 



f-r-- 

i 
<0 

f- 
.?/ 


< . .. 2-2"OA . . > f"" 




e 2" tc - '' ln " ^ """ - ^^ 


j*rf~t 

K2 


1 
T 

1 / 

I 


~ , , ' Uzshirijtitk 1 
t Lower half of head Jo ^2 JB 








J it 3 


'& / thumb-screw *s loosened 1 ^i> % 


!! 1 


/ ^ ' 
/ Half Section at A A \ Half EndVie.lv 
This edcfe of blade must be straight Detail of Thumb Scrtw for 


1-3 1 


? Clue blaJ. to u,,p f r i'^_ L>"|L| ttdjvsTn,*, 
^ halt of head ' J~ f / ' jjj^ TW f 


t of tl.fof 

<Sc/e- haffs'tie 


T 
/ '"> 

& 


- ^f 

y 
/\ 
' i 
r 

./ i/1 


* Celluloid strips each V*/Ve / \Ab/e ^"diarn. 


NoU:Gr,n of *ooJ n,u,t ie. pa r<,IM T <> T-Sc;uares Required 
^ to ed*. of UJ. Blades- Mahogany 
Edyes ofb/adei Celluloid 
- Heads Moinoqany 

Blade fa M/'cA- 







FIQ. 163 



1li < ix, (if I]*,- nil/n't ,;ji,'i xi nf_l, no matter what the scale may be. 
Thus, for example, an inch on the drawing may be marked I'-O" if 
the corresponding dimension of the object is a foot. 

Any dimension less than a foot is given in inches, not in decimal 
parts of a foot. Anything less than an inch is given by the nearest 
vulgar fraction' whose denominator is 64, 32, 16, 8, 4, or 2, not by any 
other fraction whose denominator is not one of these numbers nor by 
a decimal. Thus, for example, , f-, f, -j^, f, J|, but not $, f , |, f , etc. 

RKMAHK : Draftsmen often use decimals in comjmting dimensions, changing a frac- 
tion of nn inch to a decimal part of an inch, or inches to a decimal part of a foot, and 
/MI, by means of tables designed for that purpose. As a rule, the line between 
the numerator and denominator of a fraction should not be oblique. 



8" edge. In iron the width of a plate is at right angles to the rolled 
edge, and in many cases, as in bending, it is important to know which 
dimension is the width. 

If a dimension is in even feet, or in feet and a fraction of an inch, 
the 0" should be noted. For example, 2'-0", or I'-O", or l'-0|", not 
2', nor 1', nor !'-", nor 12". 

Dimensions should be put on the drawing as fast as tliey are used 
in making it. It is a bad plan to wait until the drawing is finished 
before putting them on, as some are apt to be omitted. 

The very same dimensions used in making the drawing (perhaps more) will prob- 
ably be needed in making the object. A draftsman needs to look at his drawing from 
the standpoint of the workman to make sure of noting all the dimensions needed. 



96 



AN INTRODUCTORY COURSE IN MECHANICAL DRAWING 



Long dimensions are put on first, and these are subdivided and 
re-subdivided as may be necessary. Care is necessary to make the 
subdivisions "foot up" the longer length. In Figure 163 the 2'-2" 
was first put on, then the 2" + l'-10" + 2" = 2'-2", and so on. 

In order that a line of dimensions may be readily footed up, it 
should, if possible, be continuous from end to end, as, for example, 
the line above referred to in Figure 163. Dimension lines should not 
cross each other when it can be avoided; if such lines must cross, do 
not mark the length of either near their point of intersection. Di- 
mension lines should stop at exactly the right place. If necessarj', 
make the dimension more definite by a note, as, for example, 2'-3" 
C to C of holes. 

Draw centre lines, such as axes of symmetry, with long and short 
dashes alternating (Art. 32 c, page 33). Many dimensions can be 
referred to such lines. Do not give unnecessary dimensions nor re- 
peat the same one in different views unless a positive gain of clearness 
is made thereby. " Over all dimensions " are of considerable import- 
ance to save the workman the trouble of "footing up" or adding 
together a number of smaller lengths. 

In certain classes of work angles are given in degrees. In others, 
however, they are given by the length of the perpendicular when the 
base is a foot. This is easily found from the natural tangent of the 
angle (Fig. 14, page 38). If it is desired to give the angle exactly 
it is sometimes necessary to assume a base of more than a foot. It 
should always be noted, therefore, whether it is a foot or more by 
giving both sides of the triangle. 

ILLUSTRATION : Let it be required to give an angle of 30. The natural tangent 
of 30 is 0.5774. If the base is a foot the perpendicular is 0.5774 of a foot. 0.5774 of a 
foot is nearly 6^| inches. Hence for an angle of 30 the rise is 6}J inches per foot. 

The size of a small hole is given by a note, as, for example: 
" Hole 1" in diameter." It often happens that when several suc- 
cessive dimensions are alike they can all be given by a single note. 
For example, suppose that there are twelve rivet holes in a straight 
line, the distance between two adjacent holes being six inches. In- 
stead of putting down the dimension 6" eleven times, draw a dimen- 



sion line parallel to the line of holes, and extending between the lines 
drawn out from the centres of the two end holes; on this line note: 

11-spaces @ 6" = 5'-6" ; or, another form, 5'-6" = ll-()" spaces. 

A drawing is usually made to scale, but if scale and dimensions as 
given do not agree, dimensions are assumed to be correct and govern 
the men in the shop. In some shops workmen are not allowed to 
scale drawings, but must use only the written dimensions. In such 
places it is not of so much importance whether the drawing is exactly 
to scale or not. In all shop drawings, however, it is absolutely essen- 
tial that each dimension be definite and correct. 

150. NOTES QUESTIONS ANSWERED.- The workman should have 
all questions which he may need to ask answered on the drawing 
itself. Notes giving all the necessary information are, therefore, an 
important part of a working drawing. Such notes are printed in the 
vacant spaces, care being taken to avoid a crowded appearance. They 
should be so printed as to be easily read from the bottom and right- 
hand edges of the sheet, /. <?., as a rule, from left to right and from 
the bottom up. An arrow is frequently used to indicate to what part 
of the object a note applies. Abbreviations are often used, such as : 
E to E (end to end), O A (over all), C to C (centre to centre), and 
many others learned only from practical experience. 

The lettering should be plain freehand, with all words and figures 
perfectly legible (Art. 33). Script writing should be avoided. 

Notes should be given stating the material used, how each part is 
to be finished, and the number of pieces required. Special directions 
pertaining to the making, painting, shipping, etc., are given in notes 
on the drawing. In the case of large structures, like bridges and 
buildings, it may also be necessary to put on notes pertaining to erec- 
tion. 

Some of the standard form of notes are as follows : 

THE HALF NOT SHOWN EXACTLY LIKE THE HALF SHOWX. 
ALL DIMENSIONS ON THIS HALF SAME AS FOE THE OTHER HALF 
EXCEPT WHEN MARKED OTHERWISE. 

ALL MATERIAL OAK UNLESS OTHERWISE MARKED. 
PLANE THE TWO ENDS TO PERFECT CONTACT. 



WOUKING DRAWINGS 



07 



CLIP CORNER 6" EACH WAY. 

ALL BOLTS " DIAM. UNLESS OTHERWISE SPECIFIED. 

BOLT TOGETHER FOR SHIPMENT. 

TWELVE PIECES LIKE THIS REQUIRED. 

These are a few of the many standard notes found on working 
drawings. They are given to call the attention of the beginner to the 
fact that there are certain customary forms for such notes. For ex- 
ample, the clause " unless otherwise marked " or " unless otherwise 
specified " is a saving clause often necessary to the first part of the 
note. To learn these notes, however, nothing is better than a study 
of good examples in actual working drawings. 

Every class of work has its own peculiar notes. For example, the machine drafts- 
man nolusfatt over when a whole piece is to have a machine finish. The bridge drafts- 
man notes Four pieces required. 3-3fark AH, 2-Mnrk AL differ only in hi-ing righto and 
lefts. (Different members of n bridge are marked with paint before leaving the shop, 
each with the letters called for on the drawing, to facilitate erection.) In the same 
way characteristic notes could be cited from other classes of work. 

Titles are printed in the lower right-hand corner of the sheet. As 
a rule, elaborate titles are to be avoided. Use freehand letters, the 
largest letters for the most important words, the next largest for the 
next important, and so on. For example : 

DETAILS OF A 

BOOK CASE 

SCALE : i SIZE 

Sheet 2 of 4 Sheets 
For material and finish, see Sheet 1 

When there are more than two sheets, number each one and give the 
total number of sheets. Notes pertaining to material, general finish, 
etc., are usually printed on one sheet only. The scale is often omitted, 



the word "scale" followed by a dash signifying that the drawing is 
to scale, but that there are reasons for not giving it. 

The notes on a drawing form a set of specifications and should be 
definite. It is more difficult to word a note so that it cannot be mis- 
understood than at first appears. The aim should be to make every- 
thing so clear and unmistakable that the most stupid man in the shop 
will understand exactly what is wanted. 

SUGGESTIONS 

If one view shows a larger portion of the object in its true shape 
and size than any other view, start that view first. 

Estimate the space each view will occupy and draw centre lines, 
allowing space enough between views for dimensions. 

Build up each view about its centre lines. 

Project lines from one view to another to save work with the scale. 

It is often impossible to complete one view at a time, and in many 
cases it is necessary to carry along two or more views simultaneously. 

Draw the main outlines first, details last. 

Be sure important measurements to centre lines, etc., are correct 
before putting in dimensions of smaller details depending on them. 

If a dimension is altered, change all dimensions related to or de- 
pending upon it to correspond. 

Order of inking: Arcs of circles, irregular curves, straight lines, 
centre lines, dimension lines, dimensions, section lining, notes, title, 
and border line. 

For directions for the use of the instruments, for precautions to 
insure neatness, hints for rapid drafting, directions for laying off 
measurements, line notation, lettering the drawing, mixing of inks, 
shade lines, section lines, tracing, blue printing, constructions for 
parabola, hyperbola, and ellipse, etc., see Chapters II. and III. 



PLATES 



THE STUDY OF A WORKING DRAWING 



WHEN a workman is making an object from a working drawing, 
he must find the answer to his questions, " What shape ?" " How 
long ?" " How wide ?" " How deep '>" " What material ?" " How put 
together?" etc., on the drawing itself. The primary object, then, of 
a working drawing is to answer questions. As an illustration of how 
the student should study such a drawing, the following questions are 
given, the answers to which are to be found on the working drawing 
of the card file (Plate I.). 

THE BOX 

Shape ? Length O. A. ? Width O. A. ? Depth O. A. ? 
Three dimensions of Top ? Bottom ? Sides ? Partition ? 
Width and depth in the clear of each compartment? 



Location and size of sliding strips for each drawer ? 
How are corners of box fitted and held together ? 



THE DRAWER 



Shape J 

Size and shape of sides? Front pieces? Back pieces? Bottom? 
How are the back and front pieces fastened to side pieces ? 
Width and location of grooves for sliding strips ? 
Location, shape, and size of handle ? 



(JENERAL DIRECTIONS 



What is glued to bottom of box ( Material for box ? Material 
for drawer ? Outside finish ? 





CARD FILE (PLATE I.) 



100 



PLATE I. 












r 










i! 


















i 1 t 


1 








( i 

' 


ii 








i 










1 

i! |! 










n 










n i 










!! 










ii 










II i 




,_j 


-- 




- J j!i- 











il '' 










il '| 










i 1 




















!i i 










' 

>! !' 










\ !! 










'i n 










'i * 










ii i> 










ii ii 










n n 


j | 




L_ 


r 


i u i 





/o' 

Top View. 



^1 
. q, d 

V.v.>.,, 



I0 f 

//I" 

Top View of Drawer. 



J! 



HI 



Make tv/dtfj of Groove to fit Sliding Str/fo. 



of Drv/wer, 



Mores. 

Alt ours'rte mater/erf /j 
c/jerry rvjbfoeaf cfnoot/7 
ar70/ joo/tGf?(*at. 

Draivers are n 

X// 'joints S/ta// be 

gect and glue cf foyet/j- 

er. 

Jp/ece of fe/r e'x//' 
AT fobeq/t/ecf to -t/ie 
bo-t-fom of fneiboX 



*--- -- *#" - --->, 



& 



"h- 



y 



End View of Drawer. 




WorKing Drawing 
of Card File. 
Scale 



f. 13. rlzZfaAfH/ c/ass o 
ield Scientific S 
Ya/e Unrt/ersity. 



Front View. 



SecT/on on Axis A A . 



101 




DRAWING DKSK MADE FKOM THE WORKING DRAWING ON THK OPPOSITE PAGE 




PLATE II. 



f.6' 



\ 34* ! 




HARD WOOOr 



-ft" 





Defoiils of Drawer. Secf ion of Desk of Corner. 

Horizontal Seclion Vertical Sect/on 
Corner. of Side and Bottom. 




Sec f ton atAA. 




^ 
J 

BB. DRAWING DESK 

Material- Clear soft pine unless 
IS0 s fated, and varnished 
Scale /"- 

E.H.L. 



103 



PLATE III. 




L.R.HOPTON , CLASS OF 1896 

SHEFFIELD SCIENTIFIC SCHOOL 

YALE UNIVERSITY 



105 



PLATE IV. 




107 



PLATE V. 




Tool ' Chest 
Isometric Projection. 

Herbert Hasf/ngs.C/ass of 93. 

Sheffie/d Scientific Schoo/ 
i/a/e University. 



109 



PLATE VI. 




PLATE XY. 











. Class of 1899 

Sheffield Scientific School of Yale University- 



111 



PLATE VII. 



SE33 

! I! 

-LJ 1 




PERSPECTIVE DRAWING 
COTTAGE 



Class of 'S9 

Sheffield Scientific School, 
LJale University. 



113 



PLATE VIII. 



SECTIONS OF SCREW THREADS 



P = P' 



' (<;h - 






V THREAD 



U.S. STANDARD THREAD 



SQUARE THREAD 



RIGHT HAND SCREW 
vVMVivV 



SCREWS AND BOLTS 
LEFT HAND SCREW RIGHT HAND SCREW MACHINE BOLT WITH STANDARD HEAD AND NUT 



/VVV 

(/"Thread 





Conventional method of 
representing threads. 



Sa. Thread 

CROSS-SECTIONS OF VARIOUS MATERIALS 




CAST IRON WROUGHT IRON STEEL 



BRASS 



LEAD 



WOOD, WITH GRAIN WOOD, ACROSS GRAIN 










115 



THIS BOOK IS DUE ON THE LAST DATE 
STAMPED BELOW 



AN INITIAL FINE OF 25 CENTS 

WILL. BE ASSESSED FOR FAILURE TO RETURN 
THIS BOOK ON THE DATE DUE. THE PENALTY 
WILL INCREASE TO SO CENTS ON THE FOURTH 
DAY AND TO $1.OO ON THE SEVENTH DAY 
OVERDUE. 



HOV 4 \*& 


Raturned by 


t 


APR 2 2 1980 


aH**** 


C'JIIIQ CrU2 .'trilb~X 


\jvw 

4 




REC'D LD 




(IP " ") c: 1Q~9 


J-" 


u o i (, o loot. 




CtEC. CIR. APR 2 ! 


! 1980 






UAD -4 1<?5S ^ 


3 


pfW 

, 





00815 




